Calculated Industries 4090 ITI Sheet Metal/HVAC Pro User Guide

S HEET M ETAL HVAC P RO

Model 4090

User’s Guide

INTRODUCTION

The custom-designed ITI Sheet Metal/HVAC Pro calculator was specifically created for sheet metal pro’s to ease the task of performing mathematics on the job. It includes the most popular built-in formulas for sheet metal computations, so you’ll save time, increase accuracy and eliminate errors.

Your Calculator Helps You Solve:

• Dimensional Math Problems

• Conversions Between Feet-Inch-Fractions, Decimal Feet,

Decimal Inches and Metric

• Problems Involving All Common Fractions – 1/2” to 1/64”

• Area/Volume Calculations

• Arc/Circle/Column/Cone Areas and Volumes

• D:M:S

• Scientific Notation, Cubed Root

• Offset Calculations

• Trigonometry

• Law of Cosines

• Fan Laws 1, 2 and 3

• Velocity/Velocity Pressure Conversions

• Right Angle/Rafter Solutions

• Stair Layout (Risers/Treads), and more!

It also includes handy construction math and material estimation examples — such as right angle/rafter and stair calculations — that will also help you build faster and more accurately.

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TABLE OF CONTENTS

KEY DEFINITIONS ............................................................................6

BASIC OPERATION KEYS .............................................................6

CONVERT Ç KEY— UNIT CONVERSIONS and

SECOND FUNCTIONS ................................................................6

MEMORY and STORAGE FUNCTIONS ........................................7

RECALL ® KEY ..........................................................................8

FEET-INCH-FRACTION and METRIC KEYS .................................8

TRIGONOMETRIC KEYS ...............................................................9

PYTHAGOREAN THEOREM/RIGHT TRIANGLE KEYS ..............10

LAW OF COSINES/NON-90 DEGREE TRIANGLE KEYS ...........12

OFFSET KEYS..............................................................................13

FAN LAW KEYS ............................................................................14

VELOCITY PRESSURE/FPM KEYS ............................................15

CIRCULAR/ARC FUNCTION KEYS .............................................15

COLUMN/CONE KEY ...................................................................16

HIP/VALLEY and JACK RAFTER KEYS.......................................17

STAIR KEY....................................................................................19

GETTING STARTED........................................................................21

ORDER OF OPERATIONS ...........................................................21

USING PARENTHESES ...............................................................22

SETTING FRACTIONAL RESOLUTION.......................................23

Setting Fraction Resolution to Other Than 16ths —

Using the Preference Setting Mode .......................................23

Setting Fixed/Constant Fractional Resolution............................24

ENTERING DIMENSIONS ............................................................25

Entering Linear Dimensions.......................................................25

Entering Square/Cubic Dimensions ...........................................25

CONVERSIONS (LINEAR, AREA, VOLUME) ..............................27

Linear Conversions ....................................................................27

Converting Feet-Inch-Fractions to Decimal Feet .......................27

Converting Decimal Feet to Feet-Inch-Fractions .......................27

Converting Fractional Inches to Decimal Inches .......................27

Converting Decimal Inches to Fractional Inches .......................28

Square Conversions ..................................................................28

Cubic Conversions .....................................................................28

PERFORMING BASIC MATH WITH DIMENSIONS....................29

Adding Dimensions ....................................................................29

Subtracting Dimensions .............................................................29

Multiplying Dimensions ..............................................................29

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Dividing Dimensions ..................................................................29

Percentage Calculations ............................................................30

MEMORY OPERATION ................................................................31

EXAMPLES — USING THE SHEET METAL/HVAC PRO ..............33

BASIC EXAMPLES .......................................................................34

Adding Linear Measurements ....................................................34

Converting Feet-Inch-Fractions to Decimal Feet and

Fractions of an Inch ................................................................34

Converting Feet-Inches to Meters and Millimeters ....................34

Adding and Subtracting Fractions of an Inch.............................35

Converting Fractions to Decimals ..............................................35

Converting Decimals to Fractions ..............................................35

Finding Length (of Iron) Required..............................................35

Circumference of a Circle ..........................................................36

Circumference and Area of a Circle...........................................36

Square Area (x 2 ).........................................................................36

Area of a Rectangle ...................................................................36

Area of a Triangle ......................................................................37

Volume of a Rectangular Box ....................................................37

Volume of a Rectangular Container, Converting to

Cubic Meters...........................................................................37

Volume of a Cylinder..................................................................38

Volume of a Cone ......................................................................38

Cubed Function..........................................................................39

Cubed Root Function .................................................................39

Scientific Notation ......................................................................39

TRIGONOMETRIC FUNCTIONS..................................................40

Finding Sine, Cosine, Tangent ...................................................41

Finding “Angle A” (ArcSin, ArcCos, ArcTan) ..............................41

Using Trigonometry to Find Unknown Side ...............................41

Using Trigonometry to Find Unknown Angle or Side.................42

Converting Pitch to Angle/Tangent.............................................45

D:M:S EXAMPLE ..........................................................................45

Converting Degrees:Minutes:Seconds ......................................45

VELOCITY PRESSURE/VELOCITY EXAMPLES.........................46

Converting Velocity Pressure to FPM ........................................46

Converting FPM to Velocity Pressure ........................................47

OFFSET EXAMPLES....................................................................48

Offset, Basic Example................................................................48

OGEE Offset in Feet-Inch-Fractions ..........................................49

OGEE Offset, in Millimeters .......................................................50

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Dividing Offset into Multiple Degreed Elbows for

Manageable Sections .............................................................51

Change OGEE Offset ................................................................53

LAW OF COSINES EXAMPLES...................................................55

Field Measuring for Ductwork Using the Law of Cosines

Introduction .............................................................................55

Non-90 Degree Triangle Measurement Using Law of Cosines and Heron’s Theorem .............................................................56

Using Law of Cosines and Pythagorean Theorem to

Calculate Offset, Length, and Angle .......................................58

Sheet Metal Panels for an Irregular Hip Roof............................59

Inline Duct, Single Offset (Computing Offset, Length, and Angle)...............................................................................60

Inline Duct, Double Offset (Computing Offset, Length, and Angle)...............................................................................62

Objects at Right Angles .............................................................65

Calculating Angles Between Objects (“Angle Between”) ...........69

Calculating Angles Between Objects Example ..........................70

FAN LAW EXAMPLES ..................................................................75

Fan Law 1 ..................................................................................75

Fan Law 2 ..................................................................................76

Fan Law 3 ..................................................................................77

ARC/CIRCLE EXAMPLES ............................................................78

Arc Length — Degree and Diameter Known .............................78

Arc Length — Degree and Radius Known .................................78

Using ArcK to Calculate an Arc Length......................................78

Arc Calculations — Arc Length and Diameter Known ...............79

Arched/Circular Rake-Walls — Chord Length and Segment

Rise Known .............................................................................80

Arched Windows ........................................................................81

CONCRETE/PAVING ....................................................................82

Squaring-up a Foundation .........................................................82

Volume of a Rectangle...............................................................82

Volume of Columns....................................................................83

RIGHT TRIANGLE and ROOF FRAMING EXAMPLES ...............84

Roof Framing Definitions ...........................................................84

Degree of Pitch ..........................................................................86

Percent Grade............................................................................86

Common Rafter Length..............................................................87

Common Rafter Length — Pitch Unknown ................................87

Angle and Diagonal (Hypotenuse) .............................................88

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Rise ............................................................................................88

Rise and Diagonal......................................................................88

Sheathing Cut ............................................................................89

Regular Hip/Valley and Jack Rafters .........................................89

Jack Rafters — Using Other Than 16 Inch On-Center

Spacing ...................................................................................91

Irregular Hip/Valley and Jack Rafters — Descending, with

On-Center Spacing Maintained ..............................................92

STAIR LAYOUT EXAMPLES ........................................................94

Stair Layout Definitions ..............................................................94

Stairs — Given Only Floor-to-Floor Rise ...................................96

Stairs — Given Only the Run .....................................................98

Stairs — Given Rise and Run ....................................................99

Baluster Spacing ......................................................................100

APPENDIX A — TRIGONOMETRY FORMULAS .........................101

APPENDIX B — AREA/VOLUME FORMULAS ............................102

AREA FORMULAS......................................................................102

SURFACE AREA/VOLUME FORMULAS ...................................103

APPENDIX C — OFFSET FORMULAS ........................................104

APPENDIX D — LAW OF COSINES/HERON’S THEOREM

FORMULAS ................................................................................105

APPENDIX E — FAN LAW FORMULAS ......................................106

APPENDIX F — DEFAULT SETTINGS .........................................106

APPENDIX G — PREFERENCE SETTINGS ................................107

How to Set Preferences ..............................................................110

Accessing Preference Settings....................................................111

APPENDIX H — CARE INSTRUCTIONS ......................................113

APPENDIX I — ACCURACY, AUTO SHUT-OFF, BATTERIES,

ERRORS .....................................................................................114

Accuracy/Errors ...........................................................................114

Auto Shut-Off...............................................................................115

Battery(ies) ..................................................................................115

Replacing the Battery(ies) ...........................................................115

Battery Replacement Instructions ...............................................115

Reset Key ....................................................................................115

REPAIR AND RETURN..................................................................116

WARRANTY ...................................................................................117

INDEX .............................................................................................119

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KEY DEFINITIONS

BASIC OPERATION KEYS

o On/Clear — Turns power on. Pressing once clears the display. Pressing twice clears all temporary values.

O

+ – x

÷ =

Ç +

Turns all power off, clearing all non-permanent registers.

Arithmetic operation keys.

Percent (%) — Four-function percent. See page 30 for examples.

0 – 9 and • Keys used for entering digits.

B Backspace Key — Used to delete entries one keystroke at a time (unlike the o function, which deletes the entire entry).

CONVERT Ç KEY —

UNIT CONVERSIONS and SECOND FUNCTIONS

The Ç key is to convert between measurement units or to access second functions, listed below:

Ç Convert — Used with the measurement keys to convert between units or with other keys to access special functions.

Ç x Clear All — Clears all values, including Memory.

Resets all permanent entries to default values

(except Preference Settings, which are retained).

Note: Use only when necessary, as it deletes all stored values.

X

Ç X

√

Squares the value in the display. For example, to

Square the value ten, enter 1 0 then press X .

x 3 — Cubes the value in the display. For example, to

Cube the value ten, enter 1 0 then press ÇX .

Square Root Function — Used to find the Square

Root of a non-dimensional or area value

(e.g., 1 0 0 √ = 10).

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Ç √

Ç /

Ç ÷

Ç –

π

Ç π

Ç •

Ç =

Cube Root Function — Used to find the Cube Root of a non-dimensional or area value (e.g., 1 0 0

0 Ç √ = 10).

x10 y — Allows entry of an exponent. For example,

8 Ç / 1 4 is 8 times 10 to the 14th power

(8x10 14 ).

1/x — Finds the reciprocal of a number (e.g., 8

Ç ÷ = 0.125).

Change (+ / –) Sign — Changes the sign of the displayed value to negative or positive.

Pi — Constant = 3.141593

ArcK — Constant = 0.017453. This value is equivalent to the constant of a 1° arc angle for a one-unit value. The formula for this constant is

π

÷ 180.

Degrees:Minutes:Seconds — Converts between

D:M:S and Decimal Degree formats.

Note: Your calculator uses a floating d:m:s format (that is, displays decimal degrees to the maximum number of decimal points, for greater accuracy). If you desire rounding to two decimal points

(0.00°), you must set your calculator via Preference Settings (see page 107 ).

Access Preference Settings — Used to access various customizable settings, such as dimensional answer formats (see Preference Settings on page

107 ).

MEMORY and STORAGE FUNCTIONS

Your calculator has two types of Memory:

μ

1) basic Memory or Semi-Permanent, Cumulative μ ;

2) non-cumulative Storage Registers (M1-M3).

Semi-Permanent Memory — Adds any displayed number, dimensioned or unitless, to the semi-permanent, accumulating Memory. Values can be subtracted from this Memory using Ç μ .

® ® will recall and clear the Memory.

Ç ® will swap the value stored in accumulative Memory with the value that is currently displayed.

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Ç 1

Ç 2

Ç 3

Storage Register (M1) — Stores the displayed value in non-cumulative, permanent Memory (e.g.,

1 0 Ç 1 , ® 1 = 10). Good for storing a single value, for future reference.

Note: Non-cumulative means it only accepts one value (does not add or subtract) and a second entered value will replace the first.

Permanent means the value is stored even after the calculator is shut off. To delete a stored value, enter a new value or perform a

Clear All ( Ç x ).

Storage Register (M2) — Same function as Ç

1 .

See above.

Storage Register (M3) — Same function as Ç

1 .

See above.

RECALL ® KEY

The ® key is used to recall or review stored values (e.g., ® p to recall a previously entered pitch value). It is also used in reviewing stored settings and Memory operation (see below).

® ®

® μ

® 1

® 2

® 3

Clear M+

Recall M+

Recall M1

Recall M2

Recall M3

— Displays and clears M+.

— Displays value stored in M+.

— Recalls the stored value in M1.

— Recalls the stored value in M2.

— Recalls the stored value in M3.

FEET-INCH-FRACTION and METRIC KEYS

The following keys are used for entering units of measure, with ease and accuracy: f Enters or converts to Feet. Also used with the i and / keys for entering Feet-Inch values (e.g., 6 f 9 i 1 / 2 ).

Note: Repeated presses after Ç toggle between Feet-Inches and

Decimal Feet (e.g., 6 f 9 i 1 / 2 Ç f = 6.791667

FEET; press f again to return to Feet-Inch-Fractions).

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/ m

Ç m

Enters or converts to Inches. Also used with the / key for entering fractional inch values (e.g., 9 i

1 / 2 ).

Note: Repeated presses after Ç toggle between Fractional and Decimal Inches (e.g., 9 i 1 / 2 Ç i = 9.5

INCH; press i again to return to Inch-Fractions).

Fraction Bar — Used to enter Fractions. Fractions may be entered as proper (1/2, 1/8, 1/16) or improper

(3/2, 9/8). If the denominator (bottom) is not entered, the calculator's fractional resolution setting is automatically used (e.g., entering 1 5 / = or + will display 15/16, based on the default fractional resolution setting of 16ths.

Meters — Enters or converts to Meters.

Millimeters — Enters or converts to Millimeters.

TRIGONOMETRIC KEYS

Tangent Ø = Opposite

Adjacent

Sine Ø = Opposite

Hypotenuse

Cosine Ø = Adjacent

Hypotenuse

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Your calculator has standard trigonometric keys, in addition to Right

Triangle keys (e.g., R , r , d and p ), for advanced Right Triangle mathematics.

The Sine, Cosine, and Tangent of an angle are defined in relation to the sides of a Right Triangle.

Using the Ç key with the trigonometric function gives you the

Arcsine, Arccosine and Arctangent – all of which are used to find the

Angle for the Sine, Cosine, or Tangent value entered.

S

Ç S

ç

Ç ç t

Ç t

Sine Function — Calculates the Sine of a Degree or undimensioned* value.

Arcsine (sin -1 ) — Calculates the angle for the entered or calculated Sine value.

Cosine Function — Calculates the Cosine of a

Degree or undimensioned* value.

Arccosine (cos -1 ) — Calculates the angle for the entered or calculated Cosine value.

Tangent Function — Calculates the Tangent of a

Degree or undimensioned* value.

Arctangent (tan -1 ) — Calculates the angle for the entered or calculated Tangent value.

*Note: Cannot use on dimensioned values.

PYTHAGOREAN THEOREM / RIGHT TRIANGLE KEYS

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Using the Pythagorean Theorem, the top row of keys on your ITI

Sheet Metal/HVAC Pro provides instant solutions in dimensional format to Right Triangle problems for sheet metal problems and roof framing.

The Right Triangle is calculated simply by entering two of four variables:

R r

1) x (Run)

2) y (Rise)

3) r (Diagonal, or Hypotenuse); or

4) θ (Theta/Pitch).

Run — Enters or calculates “x,” or the Run or horizontal leg (base) of a Right Triangle.

Rise — Enters or calculates “y,” or the Rise or vertical leg (height) of a Right Triangle.

d Hypotenuse or Diagonal (for Roof Framing) —

Enters or calculates the Hypotenuse or diagonal leg of a Right Triangle. Typical applications in construction/framing are “Squaring-up” slabs or finding

Common rafter lengths. Additional presses of the d key will also display Plumb and Level cut angles in degrees.

Note: The Common rafter calculation is the “point-to-point” length and does not include the overhang or ridge adjustment.

p Theta — Enters or calculates the Pitch (slope) of a roof (or Right Triangle). Pitch is the amount of “Rise” over 12 Inches of “Run.” Pitch may be entered as:

• a Dimension: 9 i p

• an Angle or Degrees: 3 0 p

• a Percentage (percent grade): 7 5 Ç + p

Once a Pitch in one of the above formats is entered, consecutive presses of p will convert to the remaining pitch formats listed above (e.g., Pitch in Inches will convert to Pitch Degrees, Percent Grade and

Pitch Ratio/Slope).

Note: An entered (vs. calculated) Pitch is a permanent entry. This means that it will remain stored even after you turn the calculator off. To change the Pitch, simply enter a new Pitch value.

In contrast, a calculated Pitch value is not permanently stored.

This means that the calculator will return to the Pitch value you last entered when you press o twice.

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LAW OF COSINES / NON-90 DEGREE TRIANGLE KEYS

Ç 9

Ç 4

Ç 5

Ç 6

Law of Cosines — These keys are used for non-90 degree triangle mathematics and are incorporated with Right Triangle mathematics (using “Measured” non-90 degree and “Calculated” Right Triangles), particularly, for finding the dimensional relationship of distance and alignment between two or more objects. The overall purpose of these calculations is to develop the duct and/or fittings required to fill a space.

These keys calculate the opposite angles A, B, and

C given entry of Side a, b, and c using the Law of

Cosines (see Storage Registers a, b, and c below) and triangle area using Heron’s Theorem. They also enable the computation of Right Triangle lengths “ x ,”

“ y ,” “ r ” and Theta, for determining Offset, Length, and Angle.

Press Result

5

6

7

3

4

1

2

Angle A

Angle B

Angle C

Area (using formula for Heron’s Theorem)

Redisplays entered Side a

Redisplays entered Side b

Redisplays entered Side c

Storage Register “a” — Enters Side “a” of a

Measured Triangle (e.g., if Side “a” is five feet, enter

5 f Ç 4 ).

Storage Register “b” — Enters Side “b” of a

Measured Triangle.

Storage Register “c” — Enters Side “c” of a

Measured Triangle.

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Right Triangle Functions:

R Length of Unknown Side unknown Right Triangle.

— Calculates Side “x” of r Length of Unknown Side unknown Right Triangle.

— Enters Side “y” of d Hypotenuse

“r” of unknown Right Triangle, for final determination of “x” and “y.”

— Enters “c” of Measured Triangle as p Theta — Finds unknown angle for determination of

“x” and “y.”

OFFSET KEYS

Ç (

R r

Ç 4

Offset — Calculates offset measurements, including the Centerline Radius, Wrapper Length/Stretch-out,

Heel Radius, Throat Radius and Theta, given entry of “x” (actual length), “y” (offset), and “a” (“end a”) into the keys below:

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7

4

5

8

2

3

Press

1

Result

Centerline Radius (CR)

Wrapper Length/Stretch-out (WL)

Heel Radius

Throat Radius

Theta (THET)

Redisplays entered “x” (Actual Length)

Redisplays entered “y” (Offset)

Redisplays entered “a” (Storage

Register “a” or End “a”)

Actual Length — Enters the actual length “x” for offset calculations.

Offset Length — Enters the offset “y.”

Storage Register “a” — Enters length of “end a” for offset calculations.

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FAN LAW KEYS

Your calculator also has built-in formulas and keys that calculate Fan

Laws 1, 2 and 3, for air flow calculations. Each of these formulas requires the entry of three variables in order to solve the fourth.

Ç R Fan Law 1 — Calculates the missing variable (e.g.,

“a-new” or “b-new” for CFM new or RPM new) for

Fan Law 1, given the three known variables into the applicable Storage Registers (see below). See page 75 for examples.

Ç r Fan Law 2 — Calculates the missing variable (e.g.,

“a-new” or “b-new” for CFM new or SP new) for Fan

Law 2, given the three known variables into the applicable Storage Registers (see below). See page 76 for examples.

Ç d Fan Law 3 — Calculates the missing variable (e.g.,

“a-new” or “b-new” for CFM new or BHP new) for

Fan Law 3, given the three known variables into the applicable Storage Registers (see below). See page 77 for examples.

Storage Registers Used For Fan Laws:

Ç 4 Storage Register “a”

“a” value.

— Enters “a-old” or current

Ç 7 Storage Register “a-new” new “a” value.

— Enters “a-new” or

Ç 5 Storage Register “b”

“b” value.

— Enters “b-old” or current

Ç 8 Storage Register “b-new” new “b” value.

— Enters “b-new” or

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VELOCITY PRESSURE / FPM KEYS

Ç 0 VP ß © FPM — Converts entry to Velocity (Feet per

Minute - FPM), Velocity Pressure, Metric Velocity

(MPS) and Metric Velocity Pressure (kPA).

Press

1

2

3

4

Result

Calculates Velocity (FPM) – assumes entry is Velocity Pressure

Calculates Velocity Pressure – assumes entry is Velocity (FPM)

Calculates Metric Velocity (MPS) – assumes entry is kPA

Calculates Metric Velocity Pressure

(kPA) – assumes entry is MPS

See page 46 for examples.

CIRCULAR / ARC FUNCTION KEYS

The Circle key helps you quickly solve Circular Area, Volume or Arc problems.

C Circle — Displays and calculates the following values, given an entered Circle Diameter* or Radius:

• Diameter

• Circumference

• Circle Area

*To enter a Diameter (e.g., ten feet), press 1 0 f C . To enter a radius, see below.

Ç p

Ç C

Segment Radius — Enters or calculates the Circle

Radius (e.g., 5 f Ç p ). Used to calculate

Diameter, Circumference and Circle Area (see above).

Arc Length or Degree of Arc — A multi-function key that enters or calculates Arc Length or Degree of Arc, and further solves for additional Circular/Arc values, including Arched Rake-Walls (based on the stored on-center), listed on next page.

(Cont’d)

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R r

(Cont’d)

If a Circle Diameter is entered into the C key and

Arc Degree (or Arc Length) entered into the Arc function ( Ç C ), further presses of C will display and calculate the following:

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7

4

5

8

9

2

3

Press

1

Result

Arc Length or Degree of Arc

Chord Length

Segment Area

Pie Slice Area

Segment Rise

Stored On-Center Spacing

Length of Arched Wall 1

Length of Arched Wall 2

Length of Arched Wall 3

(if applicable), etc.*

*Note: The calculator will calculate Arched Rake-Wall stud sizes with consecutive presses of the C key until it reaches the last stud.

Run (Chord Length) — Used with r or Ç p to find the Chord Length or the Radius of a Circular

Segment. If the Segment Rise and Radius have been entered, this key will display the Chord Length of the Circular Segment.

Rise — Used with R or Ç p to find the Rise or the Radius of a Circular Segment. If the Chord

Length and Radius have been entered, this key will display the Segment Rise of the Circular Segment.

COLUMN / CONE KEY

The Column and Cone functions help you quickly estimate volume and surface area of Columns or Cones.

Ç ) Column and Cone — The first and second press of

) following Ç calculate the total volume and surface area of a Column using the values stored in

C and r ; the third and fourth consecutive presses of ) calculate the total volume and surface area of a Cone .

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HIP/VALLEY and JACK RAFTER KEYS

Your calculator uses the y (rise), x (run), r (diagonal), θ (pitch), and o.c. spacing values to calculate Regular (45°) and Irregular (non-45°)

Hip/Valley and Jack rafter lengths (excluding wood thickness, etc.).

When calculating Regular and Irregular Jack rafter lengths, you will see the letters “JK” (Common Pitch side) or “IJ” (Irregular Pitch side) and the corresponding Jack number to the left of your calculator display. This will help you keep track of the descending sizes and which side the corresponding rafter is based on.

H Hip/Valley Rafter — Finds the Regular (45°) or

Irregular (non-45°) Hip/Valley rafter length.

• Regular Hip/Valley Length: After Right

Triangle/Rafter values are entered or calculated

(e.g., Pitch, Rise, Run), pressing H will calculate the length of the Regular Hip/Valley rafter.

• Irregular Hip/Valley Length: If an Irregular Pitch is entered via Ç H (see next page), pressing

H will calculate the Irregular Hip/Valley rafter length. (An Irregular or “non-standard” roof has two different Pitches/Slopes.)

(Cont’d)

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Ç H j

(Cont’d)

• Subsequent presses of the H key will also display Plumb, Level, and Cheek cut angle values in degrees.

Irregular Pitch — Enters the Irregular or Secondary

Pitch value used to calculate lengths of the Irregular

Hip/Valley and Jack rafters.

You may enter the Irregular Pitch as:

• a Dimension: 9 i Ç H

• an Angle: 3 0 Ç H

• a Percentage: 7 5 Ç + Ç H

Note: An entered Irregular Pitch can be recalled by pressing ®

Ç H .

Jack Rafters — Finds the descending Jack rafter sizes for Regular pitched roofs, based on the stored on-center spacing and previously entered or calculated Right Triangle/Rafter values (e.g., Pitch, Rise,

Run).

• The default On-Center spacing is 16 Inches. A new

On-Center spacing may be entered and permanently stored by entering an Inch value prior to performing the Jack Rafters function (e.g., 1 2 i j ). The current On-Center spacing value can be viewed by pressing ® j .

• Repeated presses of the j key will display all the rafter sizes (on the regular pitch side) as well as display the Plumb, Level, and Cheek cut angle values. Additional presses will display the rafter sizes on the Irregular Pitch side (if an Irregular Pitch was entered; see above), or repeat the previously displayed values.

Note: You may set your calculator to display the Jack rafter lengths in either ascending or descending order (see Preference

Settings on page 107 ).

Note: You may program your calculator to “mate up” the Jack rafters, rather than using the entered or default on center for both sides (see Preference Settings on page 107 ).

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Ç j Irregular Side Jacks — Operates same as j , but displays the rafter values from the irregular pitched side first.

STAIR KEY

Your calculator easily calculates stair layout solutions. Given values for r (Rise) and/or R (Run) , your calculator will calculate Riser, Tread,

Stringer and Angle of Incline values simply by pressing the s key.

s A multi-function key that uses a stored “desired”

Riser height, stored “desired” Tread width, stored

Headroom and Floor Thickness, and entered r

(Rise) and/or R (Run) values to calculate and display the following:

12

13

14

15

8

9

10

11

6

7

4

5

2

3

Press

1

Result

Riser Height

Number of Risers

Riser Overage/Underage

Tread Width

Number of Treads

Tread Overage/Underage

Stairwell Opening

Stringer Length

Angle of Incline*

Run (entered or calculated)

Rise (entered or calculated)

Stored Riser Height

Stored Tread Width

Stored Headroom Height

Stored Floor Thickness

Note: Default values are 7-1/2 Inches for Desired Riser Height and ten Inches for Desired Tread Width, ten Inches for Floor

Thickness and 6 Feet 8 Inches for Headroom.

Note: It is not possible for the calculator to include the Nose/

Overhang Measurement. Thus, you need to adjust for this measurement per local codes.

*Note: If the inclination angle exceeds the stored Rise and stored

Run ratio by 10%, the yield symbol ( steep incline.

) will light, indicating a

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Ç s

Ç = =

= =

Store Desired Riser Height — Stores a value other than the default desired stair Riser height of

7-1/2 Inches (e.g., 8 i Ç s stores an eight-inch desired stair Riser height). To recall the stored setting, press ® s .

Store Desired Tread Width — Stores a value other than the default desired stair Tread width of ten inches.

See page 107 Preference Settings to view how to use the + and – key to increase or decrease stored Tread width.

Ç = = = Store Headroom Height — Stores a value other

= = than the default desired Headroom Height of six

Feet eight Inches , for calculation of stairwell opening. See page 107 Preference Settings to view how to use the + and – key to increase or decrease stored Headroom height.

Ç = = = Store Floor Thickness — Stores a value other than

= = = the default desired Floor Thickness of ten Inches .

See page 107 Preference Settings to view how to use the + and – key to increase or decrease stored Floor Thickness.

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GETTING STARTED

You may want to practice getting a feel for your calculator keys by reading through the key definitions and learning how to enter basic

Feet-Inch-Fractions and Metric, how to store values in Memory, etc., before proceeding to the examples.

You may also want to glance at various formulas listed in the

Appendix, so you understand what mathematical calculations your calculator is programmed to perform, or common formulas you can refer to on the job. Also review specific default settings or

Preference Settings, listed in the Appendix.

ORDER OF OPERATIONS

Unlike other Calculated Industries’ calculators, which use the

Chaining Method of Operations, this calculator uses the Order of

Operation Method.

— Chaining Method (“as entered”): 10 + 4 x 5 = 70

— Order of Operations: 10 + 4 x 5 = 30

The Order of Operations method of computing is based on the following order of preference:

1) Expressions inside of parentheses

2) Single-variable functions that perform the calculation and display the result immediately (Trig functions, Square,

Square Root, Cube, Cube Root, Log, Percent, Reciprocal,

Angle Conversions)

3) Exponential function

4) Multiplication and Division

5) Addition and Subtraction

6) Equals (completes all operations)

If you need to calculate using the Chaining Method, you can change this in your calculator Preference Settings. See page 107 for instructions.

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USING PARENTHESES

Your calculator has Parentheses keys ( and ) for performing mathematical operations. (In the Order of Operations method, expressions inside of parentheses are performed first.)

The calculator offers four levels of parenthesis:

1) First parenthesis level opened – press ( for one Right-

Sided Parenthesis.

2) Second level opened – press ( a second time for two

Right-Sided Parentheses ( ( .

3) Third level opened – press ( a third time for three Right-

Sided Parentheses ( ( ( .

4) Fourth level opened – press ( a fourth time for four Right-

Sided Parentheses ( ( ( ( .

As you close each level of Parenthesis, the displayed number of

Parentheses in the upper left corner of the LCD is reduced by one, and the results of expression are displayed.

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SETTING FRACTIONAL RESOLUTION

Your calculator is set to display fractional answers in 16ths, and all examples in this User Guide are, therefore, based on 1/16ths.

However, you may select the fractional resolution to be displayed in other formats (e.g., 1/64ths, 1/32nds, etc.). Follow the two options for selecting fractional resolution below.

Setting Fraction Resolution to Other Than 16ths —

Using the Preference Setting Mode

KEYSTROKE DISPLAY

1. Access Preference Settings:

Ç = (default setting = 1/16th of an Inch) FRAC 0-1/16 INCH

2. Access Next Fraction Sub-setting:

+

+

+

+

+

+ (returns to 16ths)

FRAC 0-1/32

FRAC 0-1/64

FRAC 0-1/2

FRAC 0-1/4

FRAC 0-1/8

FRAC 0-1/16

INCH

INCH

INCH

INCH

INCH

INCH

3. To Permanently Set the Fraction Resolution You Have Selected

Above, Press o or Any Key to Exit: o 0.

4. To Recall Your Selected Fraction Resolution:

® / STD 0-1/16

INCH

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Setting Fixed/Constant Fractional Resolution

You can also program your calculator so that the displayed fraction will always show in the fractional resolution you have set (following the above instructions). That is, instead of solving for the closest fraction, it will always display the chosen fractional resolution. For example, if you have chosen 1/64ths, 1/2 will be displayed as 32/64.

If you do not use this feature, Standard Fractional Resolution will be displayed. In other words, in the above example, 1/2 will be displayed as 1/2.

To change your calculator to Fixed (or Constant) Fractional Resolution:

KEYSTROKE DISPLAY

1. Access Preference Settings:

Ç = FRAC 0-1/16

INCH

2. Press = 12 times to access Fixed/Constant Fractional Resolution setting:

= (twelfth press of = ) FRAC Std.

3. Change setting by pressing + :

+

+ (returns to Standard)

FRAC COnSt

FRAC Std.

4. To permanently set the Fixed/Constant Fractional Resolution setting, press o or any key to exit.

o 0.

5. To recall your selected Fixed/Constant Fractional Resolution setting:

®/ (default settings) STD 0-1/16

INCH

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ENTERING DIMENSIONS

Entering Linear Dimensions

When entering Feet-Inch-Fraction values, enter dimensions from largest to smallest — e.g., Feet before Inches, Inches before

Fractions. Enter Fractions by entering the numerator (top), pressing

/ (Fraction bar key) and then the denominator (bottom).

Note: If a denominator is not entered, the fractional setting value is used.

Examples (press o after each one):

DIMENSION

5 Feet 1-1/2 Inch

17.5 Meters

32 Millimeters

KEYSTROKES

5 f 1 i 1 / 2

1 7 • 5 m

3 2 Ç m

Entering Square/Cubic Dimensions

Your calculator lets you easily enter Square and Cubic values.

Simply press a dimensional unit key two times to label a number as a Square value, or three times to label a Cubic value.

Note: If you pass the desired dimensional format, keep on pressing the dimensional unit key until the desired result is displayed.

Enter Square and Cubic dimensions in the following order:

(1) Enter numerical value (e.g., 1 0 0 ).

(2) Press desired unit key (e.g., f ) to label value as “linear.”

KEYSTROKE o o

1 0 0 f

DISPLAY

100

0.

FEET

(3) Second consecutive press of unit key (e.g., f ) labels value as

“Square.”

KEYSTROKE o o

1 0 0 f f

(4) Third consecutive press of unit key labels value as “Cubic.”

DISPLAY

0.

100

SQ FEET

KEYSTROKE DISPLAY o o

1 0 0 f f f

Note: Feet-Inch format cannot be used to enter Square or Cubic values.

0.

100 CU FEET

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Examples of Square and Cubic Entry:

FEET f f — Square Feet

(e.g., 5 f f will display 5.

SQ FEET

).

f f f — Cubic Feet

(e.g., 5 f f f will display 5.

CU FEET

).

INCHES i i — Square Inches

(e.g., 5 i i will display 5.

SQ INCH

).

i i i — Cubic Inches

(e.g., 5 i i i will display 5.

CU INCH

).

METERS m m — Square Meters

(e.g., 5 m m will display 5.

SQ M

).

m m m — Cubic Meters

(e.g., 5 m m m will display 5.

CU M ).

MILLIMETERS

Ç m m — Square Millimeters

(e.g., 5 Ç m m will display 5.

SQ MM ).

Ç m m m — Cubic Millimeters

(e.g., 5 Ç m m m will display 5.

CU MM ).

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CONVERSIONS (LINEAR, AREA, VOLUME)

Linear Conversions

Convert 14 Feet to other dimensions:

KEYSTROKE DISPLAY o o

1 4 f

Ç i m *

Ç m (mm)

*Note: When performing multiple conversions, you only have to press the Ç key once (except when accessing secondary functions (Millimeters), e.g., Ç m ).

0.

14

FEET

168

INCH

4.267

M

4267.2

MM

Converting Feet-Inch-Fractions to Decimal Feet

Convert 15 Feet 9-1/2 Inches to Decimal Feet. Then convert back to

Feet-Inch-Fractions.

KEYSTROKE o o

1 5 f 9 i 1 / 2

15

FEET

9-1/2

INCH

Ç f f 15

DISPLAY

0.

15.79167

FEET

9-1/2

FEET

INCH

Converting Decimal Feet to Feet-Inch-Fractions

Convert 17.32 Feet to Feet-Inch-Fractions.

KEYSTROKE o o

1 7 • 3 2 f

Ç f

DISPLAY

0.

17.32

FEET

17

FEET

3-13/16

INCH

Converting Fractional Inches to Decimal Inches

Convert 8-1/8 Inches to Decimal Inches. Then convert to Decimal

Feet.

KEYSTROKE o o

8 i 1 / 8

Ç i f

DISPLAY

0.

8-1/8 INCH

8.125

INCH

0.677083

FEET

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Converting Decimal Inches to Fractional Inches

Convert 9.0625 Inches to Fractional Inches. Then convert to Decimal

Feet.

KEYSTROKE o o

9 • 0 6 2 5 i

Ç i f f

DISPLAY

0.

9.0625

INCH

9-1/16

INCH

0.755208

FEET

Square Conversions

Convert 14 Square Feet to other Square dimensions:

KEYSTROKE DISPLAY o o

1 4 f f Ç i m

Ç m (mm)

*For larger digit displays, the numerator section is utilized for decimal displays.

0.

2016.

SQ INCH

1.300643

SQ M

1300642.

56 *

SQ MM

Cubic Conversions

Convert 14 Cubic Feet to other Cubic dimensions:

KEYSTROKE o o

1 4 f f f Ç i m

DISPLAY

0.

24192.

CU INCH

0.396436

CU M

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PERFORMING BASIC MATH WITH DIMENSIONS

Adding Dimensions

KEYSTROKE

Add 11 Inches to 2 Feet 1 Inch:

1 1 i + 2 f 1 i = 3

FEET

DISPLAY

0

INCH

Add 5 Feet 7-1/2 Inches to 18 Feet 8 Inches:

5 f 7 i 1 / 2 + 1 8 f 8 i = 24

FEET

3-1/2

INCH

Subtracting Dimensions

KEYSTROKE

Subtract 3 Feet from 11 Feet 7-1/2 Inches:

1 1 f 7 i 1 / 2 – 3 f = 8

FEET

DISPLAY

7-1/2

INCH

Subtract 32 Inches from 81 Inches:

8 1 i – 3 2 i = 49

INCH

Multiplying Dimensions

KEYSTROKE DISPLAY

Multiply 5 Feet 3 Inches by 11 Feet 6-1/2 Inches:

5 f 3 i x 1 1 f 6 i 1 / 2 = 60.59375

SQ FEET

Multiply 2 Feet 7 Inches by 10:

2 f 7 i x 1 0 =

Dividing Dimensions

KEYSTROKE

Divide 30 Feet 4 Inches by 7 Inches:

3 0 f 4 i ÷ 7 i =

Divide 20 Feet 3 Inches by 9:

2 0 f 3 i ÷ 9 =

25

2

FEET

FEET

10

DISPLAY

3

INCH

52.

INCH

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Percentage Calculations

Percent ( Ç + ) is used to find a given percent of a number or to perform add-on, discount or division percentage calculations. You may also perform percentage calculations with dimensional units

(Feet, Inch, etc.), in any format (Linear, Square or Cubic).

Examples:

KEYSTROKE

Find 18% of 500 Feet:

5 0 0 f x 1 8 Ç +

What is 15% of $250?

2 5 0 x 1 5 Ç +

Add 10% to 137 Square Feet:

1 3 7 f f + 1 0 Ç +

Subtract 20% from 552 Feet 6 Inches:

5 5 2 f 6 i – 2 0 Ç +

Divide 350 Meters by 80%:

3 5 0 m ÷ 8 0 Ç +

90

FEET

150.7

442

DISPLAY

0

INCH

37.5

SQ FEET

FEET

0

INCH

437.500

M

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MEMORY OPERATION

Your calculator has two types of Memory operations:

1) A Standard, Cumulative, Semi-permanent Memory μ ; and

2) Three Storage Registers [M1] , [M2] and [M3] , used to permanently store single, non-cumulative values.

Memory commands are listed below.

FUNCTION

M+:

Add value to M+

Subtract value from M+

Clear M+ (displays and clears M+)

M+ Swap (swaps current value stored in M+ with displayed value)

Recall stored value

KEYSTROKES

μ

Ç μ

® ®

Ç ®

® μ

M1/M2/M3:

Store single value in M1

Store single value in M2

Store single value in M3

Clear register M1

Clear register M2

Clear register M3

Recall stored value in M1

Recall stored value in M2

Recall stored value in M3

Ç 1

Ç 2

Ç 3

0 Ç 1

0 Ç 2

0 Ç 3

® 1

® 2

® 3

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i. Basic Cumulative Memory (M+)

Example 1:

Store 100 into M+, add 200, then subtract 50. Clear the Memory:

KEYSTROKE

1 0 0 μ

2 0 0 μ

5 0 Ç μ

® ®

Note: To Clear Memory (M+):

- press ® ® ; or

- turn off the calculator.

DISPLAY

M+ 100.

M+ 200.

M– 50.

M

M

M

M+ 250.

Example 2:

Store 100 into M+, then replace this value with 200 using Memory

Swap:

KEYSTROKE

1 0 0 μ

® μ

2 0 0 Ç ®

® μ

® ®

DISPLAY

M+

M+

M+ 100.

STORED

100.

SWAP 100.

STORED

200.

M

M

M

M

M+ 200.

ii. Permanent Storage Registers (M1, M2, and M3)

Examples:

Store a rate of $175 into M1 and recall the value:

KEYSTROKE

1 7 5 Ç 1

O o

® 1 M-1

DISPLAY

M-1 175.

0.

STORED

175.

Store 1,575 Square Meters into M2 and recall the value:

KEYSTROKE DISPLAY

1 5 7 5 m m Ç 2

O o

® 2 M-2

M-2 1575.

SQ M

STORED

0.

1575.

SQ M

Note: To Clear M1-M3: Values stored in M1-M3 will remain permanently stored, even after you turn the calculator off. You will never need to clear the storage registers; simply enter a new value. However, if you wish to clear M1-M3 to “zero”:

- Enter 0 Ç 1 , 0 Ç 2 or 0 Ç 3

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EXAMPLES — USING THE SHEET METAL/HVAC PRO

The ITI Sheet Metal/HVAC Pro calculator has keys and functions labeled in common sheet metal/HVAC or construction terms. Just follow the examples and adapt the keystrokes to your specific application.

Your calculator will save you time; you don’t need to remember common formulas, as they are built into timesaving keys.

The first examples that follow provide you with mathematical problems seen in the sheet metal industry, such as computing triangle measurements using the Pythagorean Theorem or the Law of Cosines, as well as dedicated Offset, Fan Law, and Velocity functions.

The remaining examples apply to the construction trades, especially roof framing, which also depends on Right Triangle mathematics.

It is good practice to clear your calculator (press o twice) before beginning each problem. And remember to use the Backspace

( B ) key to correct entries one entry at a time.

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BASIC EXAMPLES

Adding Linear Measurements

Find the total length of the following measurements: 5 Feet 4-1/2

Inches, 8 Inches and 3.5 Meters.

KEYSTROKE

1. Add the measurements: o o

5 f 4 i 1 / 2 +

8 i +

3 • 5 m

2. Find the total:

= 17

5

6

FEET

FEET

FEET

DISPLAY

4-1/2

0-1/2

6-5/16

0.

INCH

INCH

3.5

M

INCH

Converting Feet-Inch-Fractions to Decimal Feet and Fractions of an Inch

Convert 5 Feet 7-1/2 Inches to Decimal Feet, then Decimal Inches and Inch-Fractions:

KEYSTROKE o o

5 f 7 i 1 / 2

Ç f i i

DISPLAY

0.

5 FEET 7-1/2 INCH

5.625

FEET

67.5

INCH

67-1/2 INCH

Converting Feet-Inches to Meters and Millimeters

Convert 8 Feet 6 Inches to Meters and Millimeters:

KEYSTROKE o o

8 f 6 i Ç m

Ç m (mm)

DISPLAY

0.

2.591

M

2590.8

MM

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Adding and Subtracting Fractions of an Inch

Add 1/2 Inch, 3/8 Inch and 11/16 Inch. Then subtract 5/8 Inch.

KEYSTROKE o o

1 / 2 + 3 / 8 + 1 1 / 1 6 =

– 5 / 8 =

DISPLAY

0.

1-9/16

INCH

0-15/16

INCH

Converting Fractions to Decimals

Convert 7/32 Inch and 1/3 Inch to Decimals, respectively (and round answers):

KEYSTROKE o o

7 / 3 2 Ç i

1 / 3 Ç i

DISPLAY

0.

0.21875

INCH

(Answer = 0.219”)

0.333333

INCH

(Answer = 0.33”)

Converting Decimals to Fractions

Convert 5.875 Inches and 8.545 Inches to the nearest 16ths of an

Inch:

KEYSTROKE o o

5 • 8 7 5 i Ç i

8 • 5 4 5 i Ç i

DISPLAY

0.

5-7/8

INCH

8-9/16

INCH

Finding Length (of Iron) Required

What is the length of iron required if you need twenty (20) pieces measuring 5-1/16 Inches each? If you allow 3/32 Inch for each cut, what is the new length required?

KEYSTROKE o o

5 i 1 / 1 6 x 2 0 =

μ

3 / 3 2 x 1 9 =

μ

® μ

® ® (clear Memory)

M+

DISPLAY

0.

101-1/4 INCH

M+ 101-1/4 INCH

1-25/32 INCH

M

M

M+ 1-25/32 INCH

STORED

103-1/32 INCH

M

M

M+ 103-1/32 INCH

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Circumference of a Circle

Find the Circumference of a Circle if its Radius is 8 Feet 4 Inches:

KEYSTROKE o o

8 f 4 i Ç p

C

C

DISPLAY

0.

RAD 8

FEET

4

INCH

DIA 16

FEET

8

INCH

CIRC 52

FEET

4-5/16

INCH

Circumference and Area of a Circle

Find the Area and Circumference of a Circle with a Diameter of 11

Inches:

KEYSTROKE o o

1 1 i C

C

C

DISPLAY

0.

DIA 11

INCH

CIRC 34-9/16

INCH

AREA 95.03318

SQ INCH

Square Area (x 2 )

What is the Area of a Square room with sides measuring 7 Feet 4

Inches?

KEYSTROKE o o

7 f 4 i X

DISPLAY

0.

53.77778

SQ FEET

Area of a Rectangle

What is the Area of a room measuring 12 Feet 6 Inches by 15 Feet

8 Inches?

KEYSTROKE o o

1 2 f 6 i x 1 5 f 8 i =

DISPLAY

0.

12 FEET 6 INCH

195.8333

SQ FEET

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Area of a Triangle

Find the Area of a Triangle if its base is 45 Inches and Altitude/

Height is 30 Inches.

KEYSTROKE o o

4 5 i ÷ 2 = x 3 0 i =

DISPLAY

0.

22-1/2

INCH

675.

SQ INCH

Volume of a Rectangular Box

Find the Volume of a rectangular box with Length of 15 Inches,

Width of 6 Inches and Height 9-1/2 Inches.

KEYSTROKE o o

1 5 i x 6 i x 9 i 1 / 2 =

DISPLAY

0.

855.

CU INCH

Volume of a Rectangular Container, Converting to Cubic Meters

What is the Volume of a rectangular container that measures 3 Feet by 1 Foot 9-5/8 Inches by 2 Feet 4 Inches?

KEYSTROKE

1. Find Volume in Cubic Feet: o o

3 f x 1 f 9 i 5 / 8 x 2 f 4 i =

2. Convert to Cubic Meters:

Ç m

1

FEET

12.61458

DISPLAY

3

9-5/8

0.

FEET

INCH

CU FEET

0.357205

CU M

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Volume of a Cylinder

Calculate the Volume of a Cylinder with a Diameter of 2 Feet 4

Inches and a Height of 4 Feet 6 Inches:

*Note: For a Cylinder, use the Column ) function.

KEYSTROKE DISPLAY

1. First, enter Diameter to find Circle Area: o o

2 f 4 i C

C C

0.

DIA 2 FEET 4 INCH

AREA 4.276057

SQ FEET

2. Enter Height and find Volume of Column (or Cylinder):

4 f 6 i r

Ç )

Y 4

FEET

COL 19.24226

6

INCH

CU FEET

Volume of a Cone

Calculate the Volume of a Cone with a Diameter of 3 Feet 6 Inches and a Height of 5 Feet:

KEYSTROKE

1. Find Circle Area: o o

3 f 6 i C

C C

DIA 3 FEET

AREA 9.621128

DISPLAY

6

0.

INCH

SQ FEET

2. Enter Height and find Volume:*

5 f r

Ç ) ) ) *

Y 5 FEET

CONE 16.03521

0 INCH

CU FEET

*Note: To access Cone Volume, notice you must press the ) key three times after Ç .

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Cubed Function

What is the Cubed value of 10? What is 50 3 ?

KEYSTROKE o o

1 0 Ç X

5 0 Ç X

Cubed Root Function

Example 1:

What is the Cubed Root of 100? Then, find

KEYSTROKE o o

1 0 0 Ç √

5 0 8 8 Ç √

:

DISPLAY

0.

1000.

125000.

DISPLAY

0.

4.641589

17.1995

Example 2:

What are the three dimensions of a Cube with a Volume of 2028

Cubic Inches?

KEYSTROKE o o

2 0 2 8 Ç √

DISPLAY

0.

12.65773

(Inches)

Alternate method of entry using Unit Keys:

KEYSTROKE o o

2 0 2 8 i i i

Ç √

Ç i i

DISPLAY

0.

2028

CU INCH

12-11/16

INCH

12.65773

INCH

Scientific Notation

Add 1.78 x 10 10 and 3.90 x 10 9 :

KEYSTROKE DISPLAY o o 0.

1 • 7 8 Ç / 1 0 + 3 • 9 Ç / 9 = 2.17000

10

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TRIGONOMETRIC FUNCTIONS

Trigonometric functions are available on the ITI Sheet Metal/HVAC

Pro calculator.

The drawing and formulas below list basic trigonometric formulas, for your reference:

Given side A and angle a, find:

Side C A ÷ a ç =

(i.e., 3 f ÷ 5 3 • 1 3 ç = )

Side B A x a t =

Angle b 90° – a =

Given side A and angle b, find:

Side B

Side C

Angle a

A ÷ b t =

A ÷ b S =

90° – b =

Given side B and angle a, find:

Side A

Side C

B ÷ a t =

B ÷ a S =

Given side C and angle a, find:

Side A

Side B

C x a ç =

C x a S =

Given side A and side C, find:

Angle a

Angle b

A ÷ C = Ç ç

A ÷ C = Ç S

Given side B and angle b, find:

Side C

Side A

B ÷ b ç =

B x b t =

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Finding Sine, Cosine, Tangent

Find Sine 12°, Cosine 33° and Tangent 75°:

KEYSTROKE o o

1 2 S

3 3 ç

7 5 t

DISPLAY

0.

0.207912

0.838671

3.732051

Finding “Angle A” (ArcSin, ArcCos, ArcTan)

Find Angle A if Sine A = 0.57544, Cosine A = 0.06753 and Tangent

A = 0.87421 and round to the nearest whole angle:

KEYSTROKE o o

• 5 7 5 4 4 Ç S

• 0 6 7 5 3 Ç ç

• 8 7 4 2 1 Ç t

DISPLAY

0.

35.13045° (35°)

86.12787° (86°)

41.16028° (41°)

Using Trigonometry to Find Unknown Side

Using the Pythagorean Theorem (a 2 + b 2 = c 2 ) keys, find Side a (“x”) of a Right Triangle, if Side b (“y”) is 6-1/2 Inches and Side c (“r”), the

Hypotenuse, is 12-1/16 Inches.

Note: Use the calculator’s R , r and d keys; substitute triangle legs a, b and c for

[x], [y] and [r].

KEYSTROKE o o

6 i 1 / 2 r

1 2 i 1 / 1 6 d

R

DISPLAY

0.

Y 6-1/2

INCH

R 12-1/16

INCH

X 10-3/16

INCH

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Using Trigonometry to Find Unknown Angle or Side

Example 1 — Cos A:

Solve for the unknown angle A if the two known sides are:

Side b = 15 mm

Side c = 35 mm a) Longhand Method: In this case, use the trigonometry formula:

Cos = Adjacent/Hypotenuse or cos A = b/c

KEYSTROKE o o

1 5 * ÷ 3 5 = Ç ç

Ç •

*Note: you do not have to label mm.

DISPLAY

0.

64.62307°

(64.6°)

DMS 64.37.23

b) Alternative Method (Use Pythagorean Theorem Keys):

Insert values into x, y, or r keys to solve for Theta.

KEYSTROKE o o

1 5 R

3 5 d p

Ç •

DISPLAY

0.

X 15.

R 35.

64.62307°

(64.6°)

DMS 64.37.23

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Trig Examples (Cont’d)

Example 2 — Sin A:

Solve angle A of the offset below, if the two known sides are:

Side a = 8 Inches

Side c = 25 Inches

In this case, use the trigonometry formula:

Sin = Opposite/Hypotenuse or Sin A = a/c a) Longhand/Use Sine Formula:

KEYSTROKE o o

8 ÷ 2 5 = Ç S b) Use Pythagorean Theorem Keys:

KEYSTROKE o o

8 r

2 5 d p

DISPLAY

0.

18.66292°

(18.7°)

DISPLAY

0.

Y 8.

R 25.

/ _ Ø 18.66292°

(18.7°)

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Trig Examples (Cont’d)

Example 3 — Tan A:

Find the length of the transition for a 20° angle:

Side a = 18 Inches

Side b = unknown a) Longhand Method: Use Tan = Opposite/Adjacent

KEYSTROKE DISPLAY

1. First solve for Tan 20° to find ratio, then enter in Memory: o o

2 0 t μ M+ 0.36397

0.

M

2. Solve for Side b by dividing Side a by stored ratio:

1 8 ÷ ® μ = 49.45459

M

(49.5 inches)

3. Clear Memory and clear display:

® ® o 0.

b) Use Pythagorean Theorem Keys:

KEYSTROKE o o

1 8 r

2 0 p

R

DISPLAY

0.

Y 18.

/ _ Ø 20.°

X 49.45459

(49.5 inches)

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Converting Pitch to Angle/Tangent

Find the angle and corresponding Tangent for a roof with an 8/12

Pitch:

KEYSTROKE

1. Enter Pitch: o o

8 i p

2. Convert Pitch to degrees: p

3. Find Tangent or slope: p p

/

DISPLAY

PTCH 8

0.

INCH

_ Ø 33.69007°

0.666667

D:M:S EXAMPLE

Converting Degrees:Minutes:Seconds

Convert 23°42’39” to Decimal Degrees:

KEYSTROKE o o

2 3 • 4 2 • 3 9

Ç • (degrees)

DISPLAY

0.

DMS 23.42.39

23.71083°

Convert 44.29° to degrees:minutes:seconds format:

KEYSTROKE DISPLAY o o

4 4 • 2 9 Ç • (d:m:s)

Note: Improperly formatted entries will be redisplayed in the correct convention after any operator key is pressed. For example, 30°89’ entered will be corrected and displayed at 31°29’ 0” or 31.48333°.

0.

DMS 44.17.24

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VELOCITY PRESSURE / VELOCITY EXAMPLES

The Velocity Pressure/Velocity function uses an entered value to calculate these four values:

1. Velocity (FPM)

2. Velocity (Pressure)

Number entered is assumed to be

Velocity Pressure

Number entered is assumed to be

Velocity (FPM)

3. Metric Velocity (MPS) Number entered is assumed to be

Metric Velocity Pressure (kPA)

4. Metric Velocity Pressure Number entered is assumed to be

(kPA) Metric Velocity (MPS)

The first time you perform this function, the values are displayed in the order identified above. Subsequent calculations begin with the last displayed value.

Converting Velocity Pressure to FPM

After obtaining Velocity Pressures (VP) from taking a traverse, your calculator easily converts to Feet per Minute (FPM).

For example, convert the following VPs to FPM:

0.049”

0.123”

0.027”

KEYSTROKE

1. Enter first VP and convert to FPM: o o

• 0 4 9 Ç 0 *

2. Enter second VP and convert to FPM:

• 1 2 3 Ç 0

DISPLAY

0.

FPM 886.5445

FPM 1404.608

3. Enter third VP and convert to FPM:

• 0 2 7 Ç 0 FPM 658.0887

*The VP ß © FPM function begins with the last displayed value. If FPM is not displayed with the first press of Ç 0 , continue pressing 0 until FPM is displayed.

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Converting FPM to Velocity Pressure

Calculate the Velocity Pressure (Imperial and Metric) if the FPM is

500:

KEYSTROKE

1. Enter 500 FPM to calculate Velocity: o o

5 0 0 Ç 0

2. Calculate Velocity Pressure (VP):

0 *

3. Calculate Metric Velocity (MPS):

0

DISPLAY

0.

FPM 89554.52

VP 0.015586

MPS 29.06888

4. Calculate Metric Velocity Pressure (KPA):

0 KPA 147928.99

5. Re-display entered value:

0 500.

*The VP ß © FPM function begins with the last displayed value. If FPM is not displayed with the first press of Ç 0 , continue pressing 0 until FPM is displayed.

Note: The entered value is used to calculate all four values; for calculation of Velocity

(FPM), the entered value is assumed to be VP, and for calculation of VP, the entered value is assumed to be FPM. For calculation of MPS, the entry is assumed to be kPA, and for calculation of kPA, the entry is assumed to be MPS.

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OFFSET EXAMPLES

Offset, Basic Example

If an offset is 5 Feet, the actual Length 10 Feet, and the Height of the “end A” equal to 7 Feet, calculate the Centerline Radius,

Wrapper Length, Heel Radius, Throat Radius, and Theta.

KEYSTROKE

1. Enter actual Length as “x”: o o

1 0 f R X 10

FEET

DISPLAY

0

0.

INCH

2. Enter offset Length as “y”:

5 f r

3. Enter Height of “end A” as “a”:

7 f Ç 4 A

Y 5

STORED

7

FEET

FEET

0

0

INCH

INCH

4. Calculate Centerline Radius, Wrapper Length, Heel Radius,

Throat Radius and Theta:

Ç (

(

(

(

(

RAD 6

WL 11

FEET

HEEL 9

THRT 2

FEET

7-1/8

FEET

FEET

3

9

9

INCH

INCH

INCH

INCH

THET 26.56505°

Note: If the calculated Throat Radius is less than zero, an error will be displayed (i.e.

“THRT Error”) when attempting to calculate the Offset.

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OGEE Offset in Feet-Inch-Fractions

If an offset is 12-5/8 Inches, the actual Length 45 Inches, and the

Height of the “end A” is 38 Inches, calculate the Centerline Radius,

Wrapper Length, Heel Radius, Throat Radius, and Theta.

KEYSTROKE

1. Enter actual Length as “x”: o o

4 5 i R

DISPLAY

X 45

0.

INCH

2. Enter offset Length as “y”:

1 2 i 5 / 8 r

3. Enter Height of “end A” as “a”:

3 8 i Ç 4 A

Y 12-5/8

STORED

38

INCH

INCH

4. Calculate Centerline Radius, Wrapper Length, Heel Radius,

Throat Radius and Theta:

Ç (

(

(

(

(

RAD 43-1/4

WL 47-5/16

HEEL 62-1/4

THRT 24-1/4

INCH

INCH

INCH

INCH

THET 15.67176°

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OGEE Offset, in Millimeters

If an offset is 573 Millimeters (mm), the actual Length 2045 mm, and the Height of the “end A” 1727 mm, calculate the Centerline Radius,

Wrapper Length, Heel Radius, Throat Radius, and Theta.

*Note: To save keystrokes, you do not have to label entries in mm.

KEYSTROKE

1. Enter actual Length as “x”: o o

2 0 4 5 Ç m R

DISPLAY

X 2045.

0.

MM

2. Enter offset Length as “y”:

5 7 3 Ç m r

3. Enter Height of “end A” as “a”:

1 7 2 7 Ç m Ç 4 A

STORED

Y 573.

1727.

MM

MM

4. Calculate Centerline Radius, Wrapper Length, Heel Radius,

Throat Radius and Theta:

Ç ( RAD 1967.868

MM

(1968

MM

)

( WL 2150.408

MM

(2150

MM

)

( HEEL 2831.368

MM

(2831

MM

)

( THRT 1104.368

MM

(1104

MM

)

( THET 15.65264°

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Dividing Offset into Multiple Degreed Elbows for Manageable

Sections

Solve the offset using the given variables:

Actual Length “x”: 80-1/2 Inches

Offset Length “y”: 22-9/16 Inches

A: 68 inches

Then, divide Theta into four degreed elbows; double Theta for two equal elbows.

KEYSTROKE

1. Enter actual Length as “x”: o o

8 0 i 1 / 2 R

2. Enter offset Length as “y”:

2 2 i 9 / 1 6 r

3. Enter Height of “way end A” as “a”:

6 8 i Ç 4

DISPLAY

0.

X 80-1/2

INCH

Y 22-9/16

INCH

A

STORED

68

INCH

(Cont’d)

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(Cont’d)

KEYSTROKE

5. Convert Theta to degrees:minutes:seconds:*

Ç •

DISPLAY

4. Calculate Centerline Radius, Wrapper Length, Heel Radius,

Throat Radius and Theta:

Ç (

(

(

(

(

RAD 77-7/16

WL 84-5/8

HEEL 111-7/16

THRT 43-7/16

INCH

INCH

INCH

INCH

THET 15.6571°

DMS 15.39.26

6. Multiply by two to double offset:** x 2 = DMS 31.18.51

*The angle of Theta can be used to divide the offset into degreed elbows for more manageable sections. If the angle calculated is used, there would be four (4) elbows each at 15°39’26”.

**If two (2) elbows were desired, the calculated angle can be doubled (each elbow would be 31°18’51”). Doubling Theta provides the maximum elbow size for this offset and radius combination. The total angle on either side of center can be divided into as many elbows as is required to make the offset manageable. In the case above, the maximum angle that can be divided is 31°18’51”.

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Change OGEE Offset

Solve the Change OGEE Offset below, with Wrapper Size transitions from one end to another.

A) Solve Using: a. Actual Length “x”: 52-5/8 Inches b. Offset “y”: 15-3/16 Inches c. End “a”: 34 Inches

KEYSTROKE

1. Enter actual Length as “x”: o o

5 2 i 5 / 8 R

2. Enter offset Length as “y”:

1 5 i 3 / 1 6 r

3. Enter Height of “way end A” as “a”:

3 4 i Ç 4 A

STORED

DISPLAY

X 52-5/8

Y 15-3/16

34

0.

INCH

INCH

INCH

4. Calculate Centerline Radius, Wrapper Length, Heel Radius,

Throat Radius and Theta:

Ç (

(

(

(

(

RAD 49-3/8

WL 55-1/2

HEEL 66-3/8

THRT 32-3/8

INCH

INCH

INCH

INCH

THET 16.09806°

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B) Solve Using: a. Actual Length “x”: 52-5/8 Inches b. Offset “y”: 25-3/16 Inches c. End “a”: 34 Inches

KEYSTROKE

1. Enter actual Length as “x”: o o

5 2 i 5 / 8 R

DISPLAY

X 52-5/8

0.

INCH

2. Enter offset Length as “y”:

2 5 i 3 / 1 6 r

3. Enter Height of “end A” as “a”:

3 4 i Ç 4 A

Y 25-3/16

STORED

34

INCH

INCH

4. Calculate Centerline Radius, Wrapper Length, Heel Radius,

Throat Radius and Theta:

Ç (

(

(

(

(

RAD 33-13/16

WL 60-5/16

HEEL 50-13/16

THRT 16-13/16

INCH

INCH

INCH

INCH

THET 25.57682°

“WL”, or the Wrapper, corresponds to the side of the fitting associated with the offset dimension used for the calculation. The longest

Wrapper corresponds to the side with the largest offset (y).

Caution: When working with a “Change Transitional OGEE

Offset” (Wrapper size transitions from one end to other) the length of a cheek having a slant length must be adjusted to include that slant length prior to the calculations above taking place.

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LAW OF COSINES EXAMPLES

Field Measuring for Ductwork Using the Law of Cosines —

Introduction

Dimensions taken when measuring objects in the field are taken from the plan or horizontal plane and the elevation or vertical plane of the objects. The purpose is to find the dimensional relationship of distance and alignment between two or more objects. In the Sheet

Metal Industry, these specific dimensions are identified as Length ,

Offset , and Angle .

Relationships can be established between any two objects such as ductwork, structural, penetrations, units or terminal devices. The objects are not as important as an understanding of the information required to achieve the ultimate goal of “the ability to develop the required fittings and/or parts for the system.”

Example:

Two duct lines, both 18 Inches x 12 Inches as shown in the sketch on the next page, are to be measured for a fill-in piece. Measurements of the plan view or horizontal plane are taken from both ducts to a parallel stationary object such as a wall or a structural member. The difference between these two measurements establishes the horizontal offset between the two duct lines, if any exists. The process is repeated for the elevation measurements typically using the floor below the objects (upper at 8 Feet 8 Inches, the lower 8 Feet 10-

9/16 Inches). A measurement between the two duct lines will establish length. These measurements and calculations are used to develop the duct and/or fittings required to fill the space.

Using this method we find the fill-in piece will need to be 24 Inches in length with a 9 Inch horizontal offset and a 2-9/16 Inches vertical offset.

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Non-90 Degree Triangle Measurement Using Law of Cosines and Heron’s Theorem

The Law of Cosines keys calculate the unknown angles after inputting the three known sides of a non-90 degree triangle. Triangle area is also found given the built-in formula for Heron’s Theorem.

The relationship of any side to the included angle is identified as the angles opposite the side having the same letter designation (see diagram on next page). When using this method of measuring, the user needs to keep the relationship of the sides to their included angles in perspective at all times. Because your calculator displays all three angles, the user has the discretion of identifying as they choose.

Note: As a test, rotate the letters used to identify the sides and corresponding angles clockwise on the triangle on next page, input the lengths in the appropriate key location for the new letter and display the included angles. You’ll find that the Degree of

Angles are still in the same location in relationship to the Length of Sides as before, only the letters used to identify those lengths and angles changed positions.

Using the lengths given below designated as Side a, b and c, calculate the corresponding angles A, B and C.

Side a: 38 Feet 5 Inches

Side b: 23 Feet 4-9/16 Inches

Side c: 26 Feet 1-13/16 Inches

(Cont’d)

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(Cont’d)

KEYSTROKE DISPLAY

1. Enter side a, b and c: o o

3 8 f 5 i Ç 4

0.

A

2 3 f 4 i 9 / 1 6 Ç 5

B

STORED

STORED

23

38

FEET

FEET

5

4-9/16

INCH

INCH

2 6 f 1 i 1 3 / 1 6 Ç 6

C

STORED

26

FEET

1-13/16

INCH

2. Calculate Angle A, B and C:

Ç 9

9

9

3. Calculate Triangle area:

9

/

/

_ A 101.5734°

_ B 36.59978°

/ _ C 41.8268°

AREA 299.4929

SQ FEET

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Using Law of Cosines and Pythagorean Theorem to Calculate

Offset, Length, and Angle

In field measuring, Offset, Length and Angle are the essential dimensions to the design and fabrication of the components required to fill in between objects. In some cases, no structural objects are within reach or parallel to the objects to be measured, so other methods of measuring are required.

In this method, a Triangle is formed to establish the relationship between the objects.

For the sake of identification, this Triangle, which is physically measured, will be called

“ The Measured Triangle ,” or Triangle “ I ” below, with given dimensions.

Length and Offset form a Right Angle to each other , so Triangle

“ II ”, a Right Triangle , is used to calculate these dimensions.

Note: “x” or “y” can represent either Offset or Length, the order dictated by the initial setup and perspective. In the setup, placement of the Right Triangle should always allow for the angle of “

θ

” in Triangle “ II ” to be established by simple subtraction of angle “ A 0 ” from a known angle like 180°, as in the example below.

Find Theta θ, “x,” and “y,” if the sides of the Measured Triangle “I” are: 35 Feet 8-3/4 Inches, 21 Feet 8-15/16 Inches, and 24 Feet

3-7/8 Inches. See diagram below.

b = 21' 8-15/16"

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(Cont’d)

(Cont’d)

KEYSTROKE DISPLAY

1. Enter side a, b and c: o o

3 5 f 8 i 3 / 4 Ç 4 A

STORED

2 1 f 8 i 1 5 / 1 6 Ç 5

B

STORED

35

FEET

8-3/4

0.

INCH

21

FEET

8-15/16

INCH

2 4 f 3 i 7 / 8 Ç 6 C

STORED

24

FEET

3-7/8

INCH

2. Calculate and input Theta by subtracting Angle “A” (found by the

Law of Cosines) from known angle of 180°:

1 8 0 – Ç 9

= p

/ _ A 101.5687°

78.43128

(Theta θ )

/ _ Ø 78.43128°

3. Recall stored “c” and input as “r” the Hypotenuse:

® 6 = d R 24

FEET

3-7/8

INCH

4. Calculate “x”:

R X 4

FEET

10-9/16

INCH

5. Calculate “y”: r Y 23 FEET 9-15/16 INCH

Sheet Metal Panels for an Irregular Hip Roof

A contractor is going to cover one end of an Irregular Hip Roof with sheet metal panels. The length of the roof along the eave is 98 Feet

5-1/4 Inches, the length along the left hip is 38 Feet 10-11/16

Inches, and the length along the right hip is 73 Feet 1-1/8 Inches.

Find the angles between the roof edges.

KEYSTROKE DISPLAY

1. Enter lengths:

9 8 f 5 i 1 / 4 Ç 4 A

STORED

3 8 f 1 0 i 1 1 / 1 6 Ç 5

B

STORED

98

FEET

5-1/4

INCH

38

FEET

10-11/16

INCH

7 3 f 1 i 1 / 8 Ç 6 C

STORED

73

FEET

1-1/8

INCH

2. Calculate the angles between the roof edges:

Ç 9

9

9

9

/

/

/ _ A 119.9081°

_ B 20.02713°

_ C 40.06473°

AREA 1232.046

SQ FEET

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Inline Duct, Single Offset (Computing Offset, Length, and Angle)

When working with the process of direct measure between two ducts

#1 and #2, as diagramed below, one leg of “The Measured Triangle”

“ I ” should use the larger horizontal dimension of the two ducts.

Therefore, in this scenario, the 42 Inches dimension of duct #2 is used since it is the larger of the two ducts.

To calculate the angle A 0 in “The Measured Triangle” “ I ” and the dimensions of θ1, X1, and Y1 in triangle “ II ,” follow the sequence of input given below to solve for the dimensions in question.

Note: “x” or “y” can represent either Offset or Length, the order dictated by the initial setup and perspective. In the setup, placement of the Right-Triangle should always allow for the angle of “ θ ” in triangle “ II ” to be established by simple subtraction of angle “ A 0 ” from a known angle like 180°, as in the example below.

Find Theta θ, “x”, and “y” if the sides of the Measured Triangle “I” are: 8 Feet 2-3/8 Inches, 42 Inches, and 6 Feet 10 Inches. See diagram below.

(Cont’d)

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(Cont’d)

KEYSTROKE

1. Enter side a, b, and c: o o

8 f 2 i 3 / 8 Ç 4

4 2 i Ç 5

6 f 1 0 i Ç 6

A

C

DISPLAY

STORED

STORED

0.

8

FEET

2-3/8

INCH

B

STORED

42

INCH

6

FEET

10

INCH

2. Calculate and input Theta by subtracting Degree “A” (found by the

Law of Cosines) from known angle of 180°:

1 8 0 – Ç 9

= p

/ _ A 99.94554°

80.05446

(Theta θ)

/ _ Ø 80.05446°

3. Recall stored “c” and input as “r”:

® 6 = d

4. Calculate “x”:

R

5. Calculate “y”: r

X 1

R 6

Y 6

FEET

FEET

FEET

10

2-3/16

8-3/4

INCH

INCH

INCH

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Inline Duct, Double Offset (Computing Offset, Length and Angle)

This example (see diagrams below) depicts two ducts offsetting both in the horizontal and vertical planes. Basic procedures are the same as those followed in the previous example, except a correction to the calculated length will be required at triangle “ V ”.

A) Input “Measured Triangle I” to find Triangle IV:

KEYSTROKE

1. Enter side a, b, and c: o o

2 5 0 9 Ç m Ç 4

2 0 9 6 Ç m Ç 5

1 0 6 7 Ç m Ç 6

A

B

C

STORED

STORED

STORED

DISPLAY

2509.

2096.

1067.

0.

MM

MM

MM

2. Calculate and input Theta by subtracting Degree “A” (found by the

Law of Cosines) from known angle of 180°:

1 8 0 – Ç 9

= p

/ _ A 99.82668°

80.17332

(Theta θ)

/ _ Ø 80.17332°

3. Recall stored “b”* and input as “r”:

® 5 = d R 2096.

MM

4. Calculate “x”:

R X 357.7207

MM

5. Calculate “y”: r Y 2065.249

MM

*The calculated dimension of “Yp” is a slant length on the same plane as line “b” in the elevation view. The actual length is found by forming a Right Triangle (see Triangle V).

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B) Input “Measured Triangle II” to find Triangle III:

KEYSTROKE

1. Enter side a, b, and c: o o

2 0 8 8 Ç m Ç 4

2 0 9 6 Ç m Ç 5

3 5 6 Ç m Ç 6

A

B

C

STORED

DISPLAY

0.

2088.

MM

STORED

STORED

2096.

MM

356.

MM

2. Calculate and input Theta by subtracting Degree “A” (found by the

Law of Cosines) from known angle of 90° (in this case, the Triangles form a Right Triangle):

9 0 – Ç 9

= p

/ _ A 83.83727°

6.162732

(Theta θ)

/ _ Ø 6.162732°

3. Recall stored “b” and input as “r”:

® 5 = d

4. Calculate “x”:

R

5. Calculate “y”: r

R 2096.

X 2083.887

Y 225.0112

MM

MM

MM

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C) Input Triangle V to Find Actual Length Between the Objects:

KEYSTROKE DISPLAY

1. Enter “y” from Triangle IV and enter as “r” (the Hypotenuse): o o

2 0 6 5 Ç m d R 2065.

0.

MM

2. Enter “y” from Triangle III and enter as “y”:

2 2 5 Ç m r Y 225.

MM

3. Calculate “x” for the Actual Length between the objects:

R X 2052.706

MM

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Objects at Right Angles

When you are working with objects at Right Angles, set up the

“Measured Triangles” and subsequent calculations in the same manner as the previous inline objects. Due to the vertical misalignment of the two ducts, the added step of finding the actual length will be required.

With the exception of the duct dimensions the measured lengths of

Triangle III are slant lengths. Therefore, if the calculations are processed using these dimensions the results would also be slant lengths. To find the actual lengths for “Yp” and “Xp” requires the erection of two true length Triangles. The true length Triangles will utilize “Ye” from the elevation offset as the “Y” leg of both triangles and the measured lengths of “a” and “c” as the “r” legs.

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1) Find the elevation offset “Ye” and the actual length “Xe” in D1:

KEYSTROKE DISPLAY

1. Enter sides a, b, and c: o o

7 f 9 i 7 / 1 6 Ç 4 A

2 f 2 i Ç 5

7 f 1 1 i 1 / 8 Ç 6 C

STORED

B

STORED

STORED

7

7

FEET

2

FEET

9-7/16

FEET

2

11-1/8

0.

INCH

INCH

INCH

2. Calculate and input Theta by subtracting Degree “A” (found by the

Law of Cosines) from Right Angle of 90°:

9 0 – Ç 9

=

/ _ A 78.40512°

11.59488

p

(Theta θ)

/ _ Ø 11.59488°

3. Recall stored slant length “c” and input as “r”:

® 6 = d R 7

FEET

11-1/8

INCH

4. Calculate elevation offset “Ye”: r Y 1

FEET

7-1/8

INCH

5. Calculate actual length “Xe”:

R X 7

FEET

9-3/16

INCH

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2) Find actual length “Xe” in D2:

KEYSTROKE DISPLAY

1. Enter slant length as “r”: o o 0.

1 1 f 8 i 1 3 / 1 6 d R 11 FEET

8-13/16

INCH

2. Enter calculated elevation offset from D1 as “y”:

1 f 7 i 1 / 8 r Y 1

FEET

7-1/8

INCH

3. Calculate actual length “Xe” in D2:

R X 11

FEET

7-1/2

INCH

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3) Find the horizontal length ”Xp” between the objects and the horizontal offset “Yp” between the objects:

KEYSTROKE DISPLAY

1. Enter sides a, b and c: o o

1 1 f 7 i 1 / 2 Ç 4 A

5 f 2 i Ç 5

7 f 9 i 3 / 1 6 Ç 6 C

STORED

B

STORED

STORED

7

11 FEET

5

FEET

7-1/2

FEET

2

9-3/16

0.

INCH

INCH

INCH

2. Calculate and input Theta by subtracting Degree “A” (found by the

Law of Cosines) from 180°:

1 8 0 – Ç 9

= p

/ _ A 126.8649°

53.13512

(Theta θ)

/ _ Ø 53.13512°

3. Recall stored “c” and input as “r”:

® 6 = d R 7 FEET 9-3/16 INCH

4. Calculate horizontal length “Xp” between the objects:

R X 4

FEET

7-7/8

INCH

5. Calculate horizontal offset “Yp” between the objects: r Y 6

FEET

2-9/16

INCH

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Calculating Angles Between Objects (“Angle Between”)

The Triangle, having a total of 180°, is the basic logic used to solve for the angle between two objects. To accomplish this task, two measurable Triangles are established between the objects for the purpose of finding the angles C, A, and A2, as indicated in the example below. Subtracting the sum of Angles C, A, and A2 from

180° gives us the “Angle Between” the two objects.

The calculations to solve for the next application are based on the dimensions being slant lengths as it would be in any dimensions actually taken in the field. The actual length must be established prior to finding the “Angle Between” (AB).

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Calculating Angles Between Objects Example

LEGEND

1 Existing Roof Curb to remain.

2 New 20’ x 20’ duct down through Roof

Curb to system below.

3 New Roof Top Furnace with integral curb.

4 Field measure duct required from the existing roof to new

Roof Top Furnace.

5 Existing Roof Drain to remain.

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1) Find actual length “y” between objects in D1:

KEYSTROKE DISPLAY

1. Enter side a, b, and c: o o

8 f 1 1 i 1 1 / 1 6 Ç 4

A

STORED

1 f 7 i Ç 5

8 f 8 i 1 / 8 Ç 6 C

B

8

STORED

STORED

FEET

8

11-11/16

1

FEET

FEET

7

8-1/8

0.

INCH

INCH

INCH

2. Calculate and input Theta by subtracting Degree “A” (found by the Law of Cosines) from known angle of 180°:

1 8 0 – Ç 9

= p

/ _ A 95.70871°

84.29129

(Theta θ)

/ _ Ø 84.29129°

3. Recall stored “c” and input as “r”:

® 6 = d R 8 FEET 8-1/8 INCH

4. Calculate “x”:

R

5. Calculate “y”, or actual length: r

X 0

Y 8

FEET

FEET

10-3/8

7-5/8

INCH

INCH

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2) Find actual length “y” between objects in D2:

KEYSTROKE

1 0 i 3 / 8 R

9 f 8 i 9 / 1 6 d r

3) Find actual length “y” between objects in D3:

DISPLAY

X 10-3/8

INCH

R 9

FEET

8-9/16

INCH

Y 9

FEET

8-1/8

INCH

KEYSTROKE

1 0 i 3 / 8 R

1 0 f 2 i 1 1 / 1 6 d r

DISPLAY

X 10-3/8 INCH

R 10 FEET 2-11/16 INCH

Y 10 FEET 2-1/4 INCH

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4) Input Triangle I and find Angles A and C:

KEYSTROKE DISPLAY

1. Enter side a, b, and c: o o

2 f 2 i Ç 4

1 0 f 2 i 1 / 4 Ç 5 B

9 f 8 i 1 / 8 Ç 6 C

A

STORED

STORED

STORED

10

9

2

FEET

FEET

FEET

2

2-1/4

8-1/8

0.

INCH

INCH

INCH

2. Use Law of Cosines to find Angle “A” and store in Memory 1:

Ç 9 / _ A 12.17384°

= Ç 1 M-1 12.17384°

3. Use Law of Cosines to find Angle “C” and store in Memory 2:

Ç 9 9 9 / _ C 70.36573°

= Ç 2 M-2 70.36573°

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5) Input Triangle II and find Angle A1 and the “Angle Between”:

KEYSTROKE DISPLAY

1. Enter side a2, b2, and recall c (“a2” was calculated as “y” in first section; “c” is already stored): o

8 f 7 i 5 / 8 Ç 4 A

2 f Ç 5

® 6 C

STORED

B

8

FEET

7-5/8

INCH

STORED

STORED

0.

2

FEET

0

INCH

9

FEET

8-1/8

INCH

2. Use Law of Cosines to find Angle “A2” and store in Memory 3:

Ç 9 / _ A 53.40618°

= Ç 3 M-3 53.40618°

3. Recall M1, M2, and M3 and find total:

® 1 + ® 2 + ® 3 = 135.9458°

4. Add total to M+ (regular Memory):

μ M+ 135.9458° M

5. Subtract above angle from known angle of 180° to find the Angle

Between objects (AB):

1 8 0 – ® μ = 44.05425

M

6. Convert to degrees:minutes:seconds:

Ç •

7. Clear Memory and clear display:

® ® o

DMS 44.03.15

M

0.

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FAN LAW EXAMPLES

Fan Law 1

The formula for Fan Law 1 (built into this calculator) is: where,

CFM = Feet 3 per Minute

RPM = Revolutions per Minute

Fan laws use the temporary storage registers a, b, a-new, and b-new.

Fan Law 1 calculates using the entry of the three known variables and Ç R to calculate the unknown fourth value.

Example 1:

A 1,250 CFM fan is running at 750 RPM, but it needs to supply

1,400 CFM. What is the RPM required?

DISPLAY KEYSTROKE

1. Enter current CFM into “a” old: o o

1 2 5 0 Ç 4

2. Enter new CFM into “a-new”:

1 4 0 0 Ç 7

3. Enter current RPM into “b” old:

7 5 0 Ç 5

4. Calculate new RPM or “b-new”:

Ç R RPM n

A

A n

B

STORED

STORED

STORED

0.

1250.

1400.

750.

FAN LAW1 840.

Example 2:

You set up a fan with a VFD for 14,000 CFM running at 855 RPM.

You change the RPM to 1050. What is new CFM?

DISPLAY KEYSTROKE

1. Enter current CFM into “a” old: o o

1 4 0 0 0 Ç 4

2. Enter current RPM into “b” old:

8 5 5 Ç 5

3. Enter new RPM into “b-new”:

1 0 5 0 Ç 8

4. Calculate new CFM or “a-new”:

Ç R CFM n

A

B n

B

STORED

STORED

STORED

0.

14000.

855.

1050.

FAN LAW1 17192.98

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Fan Law 2

The formula for Fan Law 2 (built into this calculator) is:

S

S where,

SP = Static Pressure

CFM = Feet 3 per Minute

Fan laws use the temporary storage registers a, b, a-new, and b-new.

Fan Law 2 calculates using the entry of the three known variables and Ç r to calculate the unknown fourth value.

Example 1:

A fan is producing 15,300 CFM at 3.2” SP. If the fan is adjusted to

14,000 CFM, what will the new SP be?

DISPLAY KEYSTROKE

1. Enter current CFM into “a” old: o o

1 5 3 0 0 Ç 4

2. Enter new CFM into “a-new”:

1 4 0 0 0 Ç 7

3. Enter current SP into “b” old:

3 • 2 Ç 5

4. Calculate new SP or “b-new”:

Ç r SP n

A

A n

STORED

STORED

B

0.

15300.

14000.

STORED

3.2

FAN LAW2 2.679311

Example 2:

After doing a traverse, you find that the duct has 1850 CFM and a

SP of 1.2”. You adjust the zone dampers and take a new SP that is

0.83. What is the new CFM?

DISPLAY KEYSTROKE

1. Enter current CFM into “a” old: o o

1 8 5 0 Ç 4

2. Enter current SP into “b” old:

1 • 2 Ç 5

3. Enter new SP into “b-new”:

• 8 3 Ç 8

4. Calculate “a-new” or new CFM:

Ç r CFM n

A

B n

B

STORED

STORED

STORED

0.

1850.

1.2

0.83

FAN LAW2 1538.58

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Fan Law 3

The formula for Fan Law 3 (built into this calculator) is: where,

BHP = Brake Horsepower

CFM = Feet 3 per Minute

Fan laws use the temporary storage registers a, b, a-new, and b-new.

Fan Law 3 calculates using the entry of the three known variables and Ç d to calculate the unknown fourth value.

Example 1:

A fan is running at 15,800 CFM using 6.3 BHP. If the CFM is increased to 20,000 CFM, what is the new BHP?

KEYSTROKE

1. Enter current CFM into “a” old: o o

1 5 8 0 0 Ç 4

2. Enter new CFM into “a-new”:

2 0 0 0 0 Ç 7

3. Enter current BHP into “b” old:

6 • 3 Ç 5

4. Calculate new BHP or “b-new”:

Ç d BHP n

A

A n

STORED

STORED

B

DISPLAY

0.

15800.

20000.

STORED

6.3

FAN LAW 3 12.77789

Example 1 (a):

For the fan above, what is the maximum CFM if a ten HP motor is used?

KEYSTROKE

1. Clear entered CFM in “a-new”:

0 Ç 7 A n

DISPLAY

STORED

0.

2. Enter new BHP into “b-new”:

1 0 Ç 8 B n

STORED

10.

3. Calculate new maximum CFM or “a-new”:

Ç d CFM n FAN LAW 3 18430.77

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ARC / CIRCLE EXAMPLES

Arc Length — Degree and Diameter Known

Find the Arc length of an 85° portion of a Circle with a 5-Foot

Diameter:

KEYSTROKE o o

5 f C

8 5 Ç C

C

DISPLAY

0.

DIA 5

FEET

0

INCH

ARC 85.00°

ARC 3

FEET

8-1/2

INCH

Arc Length — Degree and Radius Known

Find the Arc length of a Circle with a 24-Inch Radius and 77° of Arc

(77° of 360° Circle):

KEYSTROKE o o

2 4 i Ç p (Segment Radius)

7 7 Ç C

C

DISPLAY

0.

RAD 24

INCH

ARC 77.00°

ARC 32-1/4

INCH

Using ArcK to Calculate an Arc Length

Using the ArcK constant (0.017453), calculate the Arc length given

100° of a one-unit Circle. The Radius is 5 Feet.

KEYSTROKE

1. Enter Degrees and multiply: oo

100x

2. Enter Radius and multiply:

5fx

3. Recall ArcK:

Ç π

4. Calculate Arc Length:

=

0.

100.

ARCK 0.017453

8

500

FEET

FEET

DISPLAY

0

8-3/4

INCH

INCH

Note: ArcK is equivalent to the constant of a 1° Arc angle for a one-unit value. It may be multipled with a Unitless, Linear, Square or Cubic value. The formula for ArcK is

π/180.

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Arc Calculations — Arc Length and Diameter Known

Find the Arc Degree, Chord Length, Rise, Segment and Pie Slice

Area, and Segment Rise, given a 5-Foot Diameter and an Arc length of 3 Feet 3 Inches:

KEYSTROKE DISPLAY

1. Enter Circle Diameter (Note: enter Diameter into the C key): o o

5 f C DIA 5

FEET

0

0.

INCH

2. Enter Arc Length:

3 f 3 i Ç C ARC 3

FEET

3

INCH

3. Find Degree of Arc:

C

4. Find Chord Length:

C

5. Find Segment Area:

C

6. Find Pie Slice Area:

C

7. Find Segment Rise:

C

CORD 3

ARC 74.48451°

SEG 1.051381

PIE 4.0625

RISE 0

FEET

FEET

0-5/16

SQ FEET

SQ FEET

6-1/8

INCH

INCH

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Arched/Circular Rake-Walls — Chord Length and

Segment Rise Known

You’re building a Circular or Arched Rake-Wall. Given a Chord

Length of 15 Feet and a Rise of 5 Feet, find all Arc values and lengths of the Arched walls. The On-Center spacing is 16 Inches.

KEYSTROKE

1. Enter Chord Length and Segment Rise: o o

1 5 f R

5 f r

2. Calculate Radius:

Ç p

3. Find Arc Angle:

Ç C

4. Find Arc Length:

C

5. Display entered Chord Length:

C

RUN 15

RISE 5

RAD 8

ARC 19

FEET

FEET

FEET

DISPLAY

0

0

1-1/2

0.

INCH

INCH

INCH

ARC 134.76º

FEET

CORD 15

1-5/16

FEET 0

INCH

INCH

6. Find Segment Area:

C

7. Find Pie Slice Area:

C

SEG 54.19722

PIE 77.63472

SQ FEET

SQ FEET

8. Display entered Segment Rise:

C

9. Display stored On-Center spacing for the wall:

C

RISE 5

FEET

0

INCH

OC 16

INCH

*

(Cont’d)

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(Cont’d)

KEYSTROKE DISPLAY

10. Find Arched wall stud lengths:

C

C

C

C

C

AW1 4

Note: Successive presses of C will toggle to the beginning.

FEET

AW2 4

AW3 3

AW4 3

AW5 1

10-11/16

FEET

FEET

FEET

FEET

6-5/8

11-3/8

0-1/16

6-1/4

INCH

INCH

INCH

INCH

INCH

Arched Windows

Find the Radius of an Arched window with a Chord Length of 2 Feet

7 Inches and a Rise of 10-1/2 Inches. Then, find the Arc Angle, Arc

Length and Segment Area of the window.

KEYSTROKE

1. Enter Chord Length: o o

2 f 7 i R (Run)

2. Enter Rise:

1 0 i 1 / 2 r (Rise)

3. Find Radius:

Ç p

4. Find Arc Angle:

Ç C

5. Find Arc Length:

C

6. Find Segment Area:

C C

DISPLAY

0.

X 2

FEET

7

INCH

Y 10-1/2

INCH

RAD 16-11/16

INCH

ARC 136.4579°

ARC 39-3/4

INCH

SEG 235.7767

SQ INCH

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CONCRETE/PAVING

Squaring-up a Foundation

A concrete foundation measures 23 Feet 8 Inches by 45 Feet 6

Inches. Find the diagonal measurement (Square-up) to ensure the form is perfectly square.

KEYSTROKE

1. Enter sides as Rise/Run: o o

2 3 f 8 i r (Rise)

4 5 f 6 i R (Run)

2. Find the Square-up (Diagonal): d R 51

Y 23

X 45

FEET

FEET

FEET

DISPLAY

8

6

3-7/16

0.

INCH

INCH

INCH

Volume of a Rectangle

Find the Volume of a Rectangle with the following dimensions: 36

Feet 3 Inches long, by 11 Feet 6 Inches wide, by 4 Inches deep.

KEYSTROKE

1. Multiply Length by Width: o o

3 6 f 3 i x 1 1 f 6 i

2. Find Area:

=

3. Multiply by Depth to find Volume: x 4 i =

36

11

FEET

FEET

416.875

138.9583

DISPLAY

3

6

0.

INCH

INCH

SQ FEET

CU FEET

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Volume of Columns

Find the Volume of five (5) Columns, if each has a Diameter of 3

Feet 4-1/2 Inches and a Height of 11 Feet 6 Inches.

Note: Use the Column/Cone function ( Ç ) ).

KEYSTROKE

1. Find Circle Area: o o

3 f 4 i 1 / 2

C C C

3 FEET

DISPLAY

4-1/2

AREA 8.946176

0.

INCH

SQ FEET

2. Enter Height and find the total Volume for five Columns:

1 1 f 6 i r (Rise)

Ç ) x 5 =

Y 11

FEET

COL 102.881

514.4051

6

INCH

CU FEET

CU FEET

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RIGHT TRIANGLE and ROOF FRAMING EXAMPLES

Roof Framing Definitions y (Rise): The vertical distance measured from the wall’s top plate to the intersection of the pitch line and the center of the ridge.

Span: The horizontal distance or full width between the outside edges of the wall’s top plates.

x (Run): The horizontal distance between the outside edge of the wall’s top plate and the center of the ridge; in most cases this is equivalent to half of the span.

θ (Pitch): Pitch and Slope are synonymous in modern trade language. Pitch/Slope of a roof is generally expressed in two types of measurement:

1) Ratio of unit Rise to unit Run* — 7/12 or 7 Inch

2) Angle of rafters, in degrees — 30.26°

*Note: The unit rise is the number of Inches of Rise per Foot (12 Inches) of unit Run.

The unit Run is expressed as one Foot (12 Inches).

Plate: The top horizontal wall member that the ceiling joist and rafters sit on and fasten to.

Ridge: The uppermost point of two roof planes. This rafter is the uppermost rafter that all Hip, Valley, Valley Jack, and Common rafters are fastened to.

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Rafters: Rafters are inclined roof support members. Rafters include the following types:

• Common Rafter: The Common connects the plate to the ridge and is perpendicular to the ridge.

• Hip Rafter: The Hip rafter extends from the corner of two wall plates to the ridge or King rafter at angle other than 90°. The Hip rafter is an external angle of two planes.

• Valley Rafter: The Valley rafter extends from the corner of two wall plates to the ridge or King rafter at angle other than 90°.

The Valley rafter is an internal angle of two planes.

• Jack Rafters: Rafters that connect the Hip or Valley rafter to the wall plate.

• Irregular Hip/Valley Jacks: Jack rafters found in Dual-Pitch or

“Irregular” roofs.

Regular Roof: A standard roof where the Hips and/or Valleys run at

45° and have the same Pitch/Slope on both sides of the Hip and/or

Valley.

Irregular Roof: A non-standard roof where the Hips and/or Valleys bisect two different Pitches/Slopes, or have “skewed wings” or

Irregular Jacks.

Rake-Wall: A gable end wall that follows the Pitch/Slope of a roof.

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Plumb: Vertical Cut. The angle of cut from the edge of the board that allows the rafter to mate on the vertical side of the ridge rafter.

Level: Horizontal Cut. The angle of cut from the edge of the board that allows the rafter to seat flat on the wall plate.

Cheek: Side Cut(s). The angle to cut from the SIDE of the Jack rafter to match up against the Hip or Valley rafter, usually made by tilting the blade from 90°. Jack rafters typically have one Cheek cut.

If there is only one Pitch (no Irregular Pitch), the angle will be 45°. If there are two Pitches, each side will have a different Cheek cut for the Jack rafter and the angles will total 90°.

Degree of Pitch

If the Degree of Pitch is 30.45°, what is the Percent Grade, Slope and Pitch in Inches?

KEYSTROKE DISPLAY o o

3 0 • 4 5 p p p p

/

PTCH 7-1/16

0.

_ Ø 30.45°

%GRD 58.78702

SLP 0.58787

INCH

Note: To convert Pitch in Inches: Simply enter the Pitch in Inches first (e.g., 7 i p ), then continuously press the p key to calculate the Pitch conversions, as above.

Percent Grade

If the Percent Grade is 47.25%, what is the Slope, Pitch in Inches, and Degree of Pitch?

KEYSTROKE DISPLAY o o

4 7 • 2 5 Ç + * p p p p

*Note: For entering Percent Grade, you need to label the value with the Percent key.

0.

%GRD 47.25

SLP 0.4725

PTCH 5-11/16

INCH

/ _ Ø 25.29073°

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Common Rafter Length

If a roof has a 7/12 Pitch and a Span of 14 Feet 4 Inches, what is the Point-to-Point length of the Common rafter (excluding the overhang or ridge adjustment)? What are the Plumb and Level cuts?

KEYSTROKE

2. Find Plumb and Level cuts: d d

DISPLAY

1. Find Diagonal or Point-to-Point length of the Common rafter: o o

7 i p

1 4 f 4 i ÷ 2 =

R d R 8

PTCH 7

7

X 7

FEET

FEET

FEET

2

2

3-9/16

0.

INCH

INCH

INCH

INCH

PLMB 30.25644°

LEVL 59.74356°

Common Rafter Length — Pitch Unknown

Find the Common rafter length for a roof with a Rise of 6 Feet 11-1/2

Inches and a Run of 14 Feet 6 Inches. Solve for the Pitch in

Degrees and in Inches.

KEYSTROKE

Find Diagonal and Pitch: o o

6 f 1 1 i 1 / 2 r

1 4 f 6 i R d p p

Y 6 FEET

X 14

R 16

/

DISPLAY

11-1/2

FEET

FEET

6

1

PTCH 5-3/4

0.

INCH

INCH

INCH

INCH

_ Ø 25.63565°

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Angle and Diagonal (Hypotenuse)

Find the Diagonal (Hypotenuse) and Degree of Angle of a Right

Triangle that is 9 Feet high and 12 Feet long.

KEYSTROKE

1. Enter Rise and Run: o o

9 f r

1 2 f R

Y 9

X 12

FEET

FEET

DISPLAY

0

0

0.

INCH

INCH

2. Solve for Diagonal/Hypotenuse, Pitch in Inches and Degree of

Angle: d p p

R 15

FEET

0

INCH

PTCH 9

INCH

/ _ Ø 36.8699°

Rise

Find the Rise given a 7/12 Pitch and a Run of 11 Feet 6 Inches.

KEYSTROKE o o

7 i p

1 1 f 6 i R r

DISPLAY

0.

PTCH 7

INCH

X 11

FEET

6

INCH

Y 6

FEET

8-1/2

INCH

Rise and Diagonal

Find the Rise and Diagonal of a Right Triangle given a 30° Pitch and a Run of 20 Feet 4 Inches.

KEYSTROKE o o

3 0 p

2 0 f 4 i R r d

DISPLAY

0.

/ _ Ø 30.°

X 20

FEET

4

INCH

Y 11

FEET

8-7/8

INCH

R 23

FEET

5-3/4

INCH

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Sheathing Cut

You have framed an equal Pitch roof and need to apply the roof sheathing. Find the distance from the corner of the sheathing so that you can finish the Run at the Hip rafter and cut the material. The

Pitch is 6 Inches and you are using 4-Foot by 8-Foot plywood, with the 8-Foot side along the plate.

KEYSTROKE

1. Enter Pitch: o o

6 i p

2. Enter width of plywood:

4 f d

3. Find length of sheathing:

R X 3

FEET

DISPLAY

PTCH 6

R 4

FEET

0

6-15/16

0.

INCH

INCH

INCH

Regular Hip/Valley and Jack Rafters

You’re working with a 7/12 Pitch, and half your total Span is 8 Feet 5

Inches:

(1) Find Point-to-Point length and cut angles for the Common rafter;

(2) Find the length and cut angles of the adjoining Hip (or Valley) and;

(3) Find the Regular Jack rafter lengths and cut angles (Jack rafters at 16 Inches On-Center spacing).

KEYSTROKE DISPLAY

1. Find Common rafter length and Plumb and Level cuts: o o

8 f 5 i R

7 i p d d d

R 9

X 8

FEET

FEET

5

PTCH 7

8-15/16

0.

INCH

INCH

INCH

PLMB 30.25644°

LEVL 59.74356°

(Cont’d)

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(Cont’d)

KEYSTROKE DISPLAY

2. Find Hip/Valley rafter length and cut angles:

H

H

H

H

H/V 12

FEET

10-1/2

INCH

PLMB 22.41512°

LEVL 67.58488°

CHK1 45.°

3. Find Jack rafter lengths and cut angles: j j j j j j j j j j j

JKOC 16

INCH

*

JK1 8

FEET

2-3/8

INCH

JK2 6

FEET

7-7/8

INCH

JK3 5

FEET

1-3/8

INCH

JK4 3

FEET

6-13/16

INCH

JK5 2

FEET

0-5/16

INCH

JK6 0

FEET

5-13/16

INCH

JK7 0

FEET

0

INCH

PLMB 30.25644°

LEVL 59.74356°

CHK1 45.°

*Note: If display does not read JKOC 16 INCH (the default), then enter 16 Inches prior to beginning calculation (e.g., 1 6 i j ).

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Jack Rafters — Using Other Than 16 Inch On-Center Spacing

A roof has a 9/12 Pitch and a Run of 6 Feet 9 Inches. Find the Jack rafter lengths and cut angles at 18-Inch (versus 16-Inch) On-Center spacing. The On-Center spacing is used for both Regular and

Irregular Jack calculations.

KEYSTROKE

1. Enter Pitch, Run, and On-Center spacing: o o

9 i p

6 f 9 i R

1 8 i j j

2. Find Jack rafter lengths and cut angles: j j j j j j j j

3. Reset On-Center spacing to 16 Inches:

1 6 i j

JKOC

DISPLAY

PTCH 9

X 6

FEET

STORED

9

18

0.

INCH

INCH

INCH

JK1 6

FEET

6-3/4

INCH

JK2 4

FEET

8-1/4

INCH

JK3 2

FEET

9-3/4

INCH

JK4 0

FEET

11-1/4

INCH

JK5 0

FEET

0

INCH

PLMB 36.8699°

LEVL 53.1301°

CHK1 45.°

JKOC 16

INCH

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Irregular Hip/Valley and Jack Rafters — Descending, with

On-Center Spacing Maintained

You’re working with a 7/12 Pitch and half your overall Span is 4

Feet. The Irregular Pitch is 8/12, and 16-Inch On-Center spacing is maintained on both sides. Complete the following steps:

(1) Find the length of the Common rafter;

(2) Reset calculator to 16-Inch On-Center spacing;

(3) Enter the Irregular Pitch; find the length of the adjoining

“Irregular” Hip (or Valley) and the cut angles;

(4) Find the Jack lengths on the “Irregular” Pitch side (16-Inch

On-Center spacing);

(5) Find the cut angles;

(6) Find the Jack lengths on the “Regular” Pitch side (16-Inch

On-Center spacing);

(7) Find the cut angles.

KEYSTROKE

1. Find Common rafter length: o o

7 i p

4 f R d

2. Enter On-Center spacing:

1 6 i j

R 4

DISPLAY

PTCH 7

X 4

FEET

FEET

0

7-9/16

JKOC 16

0.

INCH

INCH

INCH

INCH

3. Find Irregular Hip/Valley rafter length and cut angles:

8 i Ç H

H

H

H

H

H

IH/V 5

FEET

IPCH 8

9-11/16

INCH

INCH

PLMB 23.70162°

LEVL 66.29838°

CHK1 41.18592°

CHK2 48.81408°

4. Find Irregular Jack lengths:

Ç j j * j j

IJOC

STORED

16

INCH

IJ1 2

FEET

9-5/8

INCH

IJ2 1

FEET

4-13/16

INCH

IJ3 0

FEET

0

INCH

*Note: It is not necessary to continue pressing Ç when displaying each Jack rafter size.

(Cont’d)

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(Cont’d)

KEYSTROKE DISPLAY

5. Find Irregular Jack Plumb, Level, and Cheek cut angles: j j j

PLMB 33.69007°

LEVL 56.30993°

CHK1 41.18592°

6. Find Regular Jack lengths: j j j j

JKOC

STORED

16

INCH

JK1 2

FEET

10-3/8

INCH

JK2 1

FEET

1-1/4

INCH

JK3 0

FEET

0

INCH

7. Find Regular Jack Plumb, Level, and Cheek cut angles: j j j

PLMB 30.25644°

LEVL 59.74356°

CHK1 48.81408°

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STAIR LAYOUT EXAMPLES

Stair Layout Definitions y (Rise): The “floor-to-floor” or “landing-to-landing” Rise is the actual vertical Rise required for building a stairway after the finish flooring has been installed.

x (Run): The Run of a stairway is the amount of horizontal space required. The total Run of a stairway is equal to the width of each

Tread multiplied by the number of Treads.

Desired Riser Height: The desired Riser height is the amount of vertical Rise you allow for each individual Riser in the stairway. This is sometimes dictated by local code.

Actual Riser Height: The actual height of each Riser is measured from the top of one Tread to the top of the next Tread.

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Number of Risers: The number of Risers includes both the first and the last Riser of the stairway.

Riser Overage or Underage: The Riser Overage or Underage is the difference between the “floor-to-floor” Rise and the total height of all of the Risers. Many times the Riser height does not divide evenly into the floor-to-floor Rise and a small fraction of an Inch is left over.

A positive remainder is an Overage, while a negative remainder is an Underage.

Tread Width: The width of each Tread is measured from the front of one Riser to the front of the next Riser. The width of each Tread does NOT include the nosing or overhang of the Tread. The nosing or overhang of a Tread is the rounded front of the Tread that projects beyond the face of the Riser.

Number of Treads: The number of Treads is one less than the number of Risers.

Tread Overage or Underage: The Tread Overage or Underage is the difference between the Run or horizontal space that a stairway must fit into and the total width of the Treads. Similar to the Riser

Overage/Underage, many times the total width of the Treads does not divide evenly into the Run or horizontal space for the stairway and a small fraction of an Inch is left over. A positive remainder is an

Overage, a negative remainder is an Underage.

Stringer: Also called a Carriage, Stair Horse, or Stair Jack. A Stringer is the diagonal member that supports the Treads and Risers.

Angle of Incline: The angle of incline of the stairway is determined by the Rise and Run of each stair. The angle of incline should not be confused with the Pitch of the stairway. The Pitch of a stairway is the angle based on the floor-to-floor Rise and the horizontal Run of the stairway. The angle of incline is based on the “actual” Riser height and the “actual” Tread width of the stair.

Stairwell Opening: The length of the opening at the top of the stairs. The computation is based on the Headroom Height (the desired spacing between the stairs and upper floor ceiling) and thickness of the upper floor where the opening is located.

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Stairs — Given Only Floor-to-Floor Rise

You’re building a stairway with a total Rise of 9 Feet 11 Inches. Your desired Riser height is 7-1/2 Inches and desired Tread width is 10

Inches. The desired Headroom is 6 Feet 8 Inches and Floor

Thickness 10 Inches*. Find all stair values, then calculate the Run.

*Note: Headroom and Floor Thickness are required to calculate the height of the stairwell opening.

KEYSTROKE

1. Enter known Rise: o o

9 f 1 1 i r Y 9

2. Recall (default) stored “desired” stair Riser height:

® s R-HT

STORED

FEET

DISPLAY

11

7-1/2

0.

INCH

INCH

3. Find Riser height, number of Risers, Riser Overage/Underage,

Tread width, number of Treads, Tread Overage/Underage, length of stairwell opening, Stringer length and Angle of Incline. As a final step, calculate the Run: s s s s s s s s s s s *

STRG 15

RISE ( Y )

R-HT 7-7/16

OPEN 10

FEET

STORED

9

INCH

RSRS 16.

R+/– 0

T-WD 10

INCH

INCH

TRDS 15.

T+/– 0

FEET 1

6-15/16

INCH

INCH

INCH

INCL 36.64003°

RUN 12 FEET

FEET

6

11

INCH

INCH

*Continuous presses of s will also recall stored desired Riser height, Tread,

Headroom and Floor Thickness values.

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To Change Desired Riser Height: If you wish to use a desired

Riser height of other than 7-1/2 Inches (the calculator’s default), simply enter a new value. For example, to enter eight Inches, enter 8 i Ç s . Press ® s to review your new entry. This value will be permanently stored until you change it.

To Change Desired Tread Width: If you wish to use a desired

Tread width of other than ten Inches (the calculator’s default), simply select a new value via the Preference Mode (press Ç , then = four times and use the + or – keys to increase/decrease by 1/4

Inch increments). This value will be permanently stored until you change it.

To Change Desired Headroom: If you wish to use a desired

Headroom other than six Feet eight Inches (the calculator’s default), simply select a new value via the Preference Mode (press Ç , then = five times and use the + or – keys to increase/decrease by one-Inch increments). See below example. This value will be permanently stored until you change it.

To Change Desired Floor Thickness: If you wish to use a desired

Floor Thickness of other than ten Inches (the calculator’s default), simply select a new value via the Preference Mode (press Ç , then = six times and use the + or – keys to increase/decrease by one-Inch increments). This value will be permanently stored until you change it.

KEYSTROKE

1. Select Headroom via Preference Mode: o o

Ç = = = = =

2. Decrease Headroom Height by two Inches:

– –

HDRM 6

HDRM 6

FEET

FEET

DISPLAY

8

6

0.

INCH

INCH

3. Then increase Headroom Height by four Inches:

+ + + + HDRM 6 FEET 10 INCH

4. Return Headroom Height to default of six Feet eight Inches:

– – HDRM 6

FEET

8

INCH

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Stairs — Given Only the Run

You’re building a stairway with a total Run of 20 Feet. Your desired

Riser height is 7-1/2 Inches and desired Tread width is ten Inches

(default, or preset values). The desired headroom is 6 Feet 8 Inches and floor thickness 10 Inches (defaults). Find all stair values, then calculate the Rise.

KEYSTROKE

1. Enter Run: o o

2 0 f R X 20

FEET

DISPLAY

0

0.

INCH

2. Find Riser height, number of Risers, Riser Overage/Underage,

Tread width, number of Treads, Tread Overage/Underage, stairwell opening, Stringer length and Angle of Incline. As a final step, calculate the Rise: s s s s s s s s s s s

RUN (

X

)

OPEN 10

STRG 25

STORED

R-HT 7-1/2

INCH

RSRS 25.

R+/– 0

T-WD 10

INCH

INCH

TRDS 24.

T+/– 0

FEET

FEET

0

0

INCH

INCH

INCH

INCL 36.8699°

20

FEET

0

INCH

RISE 15

FEET

7-1/2

INCH

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Stairs — Given Rise and Run

You need to build a stairway with a floor-to-floor height of 10 Feet 1

Inch, a Run of 15 Feet 5 Inches, and a nominal desired Riser height of 7-1/2 Inches (default). Calculate all stair values.

KEYSTROKE

1. Enter Rise and Run: o o

1 0 f 1 i r

1 5 f 5 i R

Y 10

X 15

FEET

FEET

DISPLAY

1

5

0.

INCH

INCH

2. Find stair values: s s s s s s s s s s s s s s s

HDRM

R-HT 7-9/16

INCH

*

RSRS 16.

R+/– 0

INCH

T-WD 12-5/16

INCH

TRDS 15.

T+/– – 0-5/16

INCH

OPEN 12

FEET

2-1/2

INCH

STRG 18

FEET

0-3/4

INCH

RUN (

X

)

RISE (

Y

)

STORED

STORED

R-HT

INCL 31.5588°

15

FEET

5

INCH

10

FEET

1

INCH

STORED

7-1/2

INCH

T-WD

STORED

FLOR

STORED

STORED

10

INCH

6

FEET

8

INCH

10

INCH

*A yield symbol ( ) will light in the display meaning the calculated Riser height exceeds the stored desired Riser height by 10%.

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Baluster Spacing

You are going to install a handrail at the top of a balcony. Your total

Span is 156 Inches and you would like the space between the balusters to be about 4 Inches. If each baluster is 1-1/2 Inches wide, what is the exact spacing between each baluster?

KEYSTROKE DISPLAY

1. Estimate number of balusters in Span: o o

1 5 6 i ÷

5 i 1 / 2 = *

*desired spacing plus baluster width (4 Inches plus 1-1/2 Inches).

0.

156

INCH

28.36364

(28 balusters)

2. Find total space ‘occupied’ by the balusters by multiplying the width of each baluster by the rounded number of balusters (found above):

1 i 1 / 2 x

2 8 =

1-1/2

42

INCH

INCH

3. Find total space between all balusters:

1 5 6 i –

4 2 i =

156

114

INCH

INCH

4. Find actual baluster spacing by dividing total space between all balusters by the number of spaces between the balusters (number of balusters plus one equals 29):

1 1 4 i ÷

2 9 =

114

3-15/16

INCH

INCH

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APPENDIX A — TRIGONOMETRY FORMULAS

The Sine of an angle is the ratio of the opposite side over the

Hypotenuse:

Sine Sin =

Opposite

Hypotenuse c

A b a sin A = a c

The Cosine of an angle is the ratio of the adjacent side over the

Hypotenuse:

Cosine Cos =

Adjacent

Hypotenuse c

A b a cos A = b c

The Tangent of an angle is the ratio of the opposite side over the adjacent side:

Tangent Tan =

Opposite

Adjacent c

A b a tan A = a b

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APPENDIX B — AREA / VOLUME FORMULAS

AREA FORMULAS

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SURFACE AREA / VOLUME FORMULAS

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APPENDIX C — OFFSET FORMULAS

With Offset = “y” and Length = “x,”

θ = ArcSin

( Offset

SlantLength

)

= ArcTan

( Offset )

Length

= ArcTan

( ) x

CenterlineRadius =

SlantLength

4Sin(θ)

=

SlantLength 2

4 * Offset

WrapperLength (aka StretchOut) = CenterlineRadius * ArcK * 4θ

HeelRadius = CenterlineRadius + (a ÷ 2)

ThroatRadius = CenterlineRadius – (a ÷ 2)

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APPENDIX D — LAW OF COSINES / HERON’S

THEOREM FORMULAS

Law of Cosines

A c b a 2 = b 2 + c 2 – 2bccosA b 2 = c 2 + a 2 – 2cacosB c 2 = a 2 + b 2 – 2abcosC

B a C

Law of Sines

C

A b c a

R

B a sin A

= b sin B

= c sin C

= 2R

Heron’s Theorem s =

1

2

(a + b + c)

Tan

( )

=

2 r s – a

Tan

( )

=

2 r s – b

Tan

( )

=

2 r s – c

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APPENDIX E — FAN LAW FORMULAS

Fan Law 1 Formula where,

CFM = Feet 3 per Minute

RPM = Revolutions per Minute

Fan Law 2 Formula

S

S where,

SP = Static Pressure

CFM = Feet 3 per Minute

Fan Law 3 Formula where,

BHP = Brake Horsepower

CFM = Feet 3 per Minute

APPENDIX F — DEFAULT SETTINGS

After a Full Reset/Clear All, your calculator will return to the following settings:

SETTING

On-Center Spacing

Fractional Resolution

Area Display

Volume Display

Desired Riser Height

Desired Tread Width

Stairway Headroom

Floor Thickness (Stairs)

Jack Rafters

Irregular Jack Spacing

Exponent

Meter Linear Rounding

Degree Rounding

Mathematical Operations

IMPERIAL

16 Inches

1/16

Standard

Standard

7-1/2 Inches

10 inches

6 Feet 8 Inches

10 Inches

Descending

OC-OC

On

0.000

Float

Order of Operations Method

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APPENDIX G — PREFERENCE SETTINGS

Your calculator has Preference Settings that allow you to customize or set desired dimensional formats and calculations. See the list of

Settings below and instructions how to set them on the following page.

If you replace your batteries or perform a Full Reset * (press O , hold down x , and press o ), your calculator will return to the following settings (in addition to those listed on the previous page):

PREFERENCE

1) Fractional Resolution

2) Area Display Format

OPTIONS

— * 1/16 (displays fractional values to the nearest 16th of an Inch)

— 1/32

— 1/64

— 1/2

— 1/4

— 1/8

— * Standard (if units entered are the same — e.g., Feet x Feet — the answer will remain in this format (Square Feet), but if units entered are different — e.g.,

Inches x Feet — area answer will be displayed in Square Feet )

— Square Feet (area answers always displayed in Square Feet, regardless of unit entry — e.g., Inches x Inches =

Square Feet)

— Square Meters (area answers always displayed in Square meters — e.g., Feet x Feet = Square Meters)

(Cont’d)

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(Cont’d)

PREFERENCE OPTIONS

3) Volume Display Format — * Standard (if units entered are the same — e.g., Feet x Feet x Feet — the answer will remain in this format (Cubic

Feet), but if units entered are different

— e.g., Feet x Feet x Inches — volume answer will always be displayed in

Cubic Feet )

— Cubic Feet (volume answers always displayed in Cubic Feet, regardless of unit entry — e.g., Inches x Inches x

Inches = Cubic Feet)

— Cubic Meters (volume answers always displayed in Cubic Meters, regardless of unit entry — e.g., Feet x

Feet x Feet = Cubic Meters)

4) Tread Width

5) Stairwell — Headroom — * 6 Feet 8 Inch (default)

Height — Use + or – key to increase or decrease above value by increments of

1 Inch

6) Floor Thickness

— * 10 Inch (default)

— Use + or – key to increase or decrease above value by increments of

1/4 Inch

— * 10 Inch (default)

— Use + or – key to increase or decrease above value by increments of

1 Inch

7) Jack Rafters — * Descending (Jack rafters are

Descending or Ascending displayed from largest to smallest size)

— Ascending (Jack rafters are displayed from smallest to largest size)

(Cont’d)

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(Cont’d)

PREFERENCE OPTIONS

8) Irregular Jack Rafters — * OC-OC (On-Center spacing

O-C or Mate maintained on both Regular and

Irregular sides)

— JAC-JAC (Regular/Irregular Jack rafters “mate” at the Hip/Valley, i.e., On-

Center spacing not maintained on both sides)

9) Exponent Off or On — * On (Exponential Mode is On; turns on Auto-Ranging; i.e., if display can’t show seven digits, will display in next largest unit)

— Off (Exponential Mode is Off)

10) Meter Linear Display — * 0.000

(Linear Meter answers always displayed to third decimal place)

— FLOAT (Linear Meter answers displayed to the maximum number of decimal points, as entered — e.g., 1.234

Meters + 2.56 Meters = 3.794 Meters)

11) Degrees Displayed — * FLOAT

— 0.00°

12) Mathematical

Operations

— * Order (Order of Operations Method of Calculating)

— Chain (Chain Method)

13) Fractional Mode — * Standard (fractions are displayed to the nearest fraction)

— * Constant (fractions are displayed in the set fractional resolution)

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How to Set Preferences

The following sections detail Preference Setting options.

Enter the Preference Mode by pressing Ç = (Prefs) . Access each category by pressing the = key until you reach the desired setting.

Within each category, press the + or – keys to toggle between individual selections. Press o to exit and set in your

Preference.

Note: + will advance, – will back up. Pressing the = key continuously in this mode will revolve the Preference Settings full circle.

You may change these settings at any time by repeating the above, and setting in a new preference. Or, you may review settings by pressing ® = .

For example, if you wish to display all your dimensional area answers in Square Meters, press Ç = = (Area Std) , then the + key until “ AREA 0.

SQ M ” is displayed. Simply exit this mode by pressing o or any key, and all your future area answers will be displayed in Square Meters.

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Accessing Preference Settings

To Set “Fractional Resolution”:

KEYSTROKE

Ç = (Prefs) (first press of = )

+ (plus sign)

+

+

+

+

To Set “Area” Answer Format:

KEYSTROKE

= (second press of = )

+ (plus sign)

+

To Set “Volume” Answer Format:

KEYSTROKE

= (third press of = )

+ (plus sign)

+

DISPLAY

FRAC 0-1/16 INCH

FRAC 0-1/32 INCH

FRAC 0-1/64 INCH

FRAC 0-1/2 INCH

FRAC 0-1/4 INCH

FRAC 0-1/8 INCH

DISPLAY

AREA Std.

AREA 0.

SQ FEET

AREA 0.

SQ M

DISPLAY

VOL Std.

VOL 0.

CU FEET

VOL 0.

CU M

To Increase or Decrease Tread Width from Default of 10”:

KEYSTROKE DISPLAY

= (fourth press of = )

+ * (plus sign increases height by 1/4 Inch)

– * (minus sign decreases height by 1/4 Inch)

T-WD 10

T-WD 10-1/4

T-WD 10

*Keep pressing plus or minus to increase or decrease 1/4 Inch at a time.

INCH

INCH

INCH

To Increase or Decrease Stairwell “Headroom” from Default of 6’8”:

KEYSTROKE DISPLAY

= (fifth press of = )

+ * (plus sign increases height by 1 Inch)

HDRM 6

HDRM 6

FEET

FEET

8

9

INCH

INCH

– * (minus sign decreases height by 1 Inch) HDRM 6

FEET

8

INCH

*Keep pressing plus or minus to increase or decrease an Inch at a time.

(Cont’d)

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(Cont’d)

To Increase or Decrease Floor Thickness from Default of 10”:

KEYSTROKE DISPLAY

= (sixth press of = )

+ * (plus sign increases height by 1 Inch)

– * (minus sign decreases height by 1 Inch)

FLOR 10

FLOR 11

FLOR 10

*Keep pressing plus or minus to increase or decrease an Inch at a time.

INCH

INCH

INCH

To Set Jack Rafter to “Descending” or “Ascending”:

KEYSTROKE

= (seventh press of = )

+ (plus sign)

DISPLAY

JACK dESCEnd

JACK ASCEnd

To Set Irregular Jack Spacing to “On-Center” or “Mate”:

KEYSTROKE

= (eighth press of = )

+ (plus sign)

DISPLAY

IRJK OC-OC

IRJK JAC-JAC

To Set “Exponential Mode” On or Off:

KEYSTROKE

= (ninth press of = )

+ (plus sign)

DISPLAY

EXP On

EXP OFF

To Set “Meter” Linear Decimal Format:

KEYSTROKE

= (tenth press of = )

+ (plus sign)

To Set “Degrees” Rounding/Display:

KEYSTROKE

= (eleventh press of = )

+ (plus sign)

DISPLAY

METR 0.000

M

METR FLOAt

M

DISPLAY

DEG FLOAt

DEG 0.00°

(Cont’d)

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(Cont’d)

To Set Mathematical Operations Method:

KEYSTROKE

= (twelfth press of = )

+ (plus sign)

To Set Fractional Mode:

DISPLAY

MATH OrdEr

MATH CHAIn

KEYSTROKE DISPLAY

= (thirteenth press of = )

+ (plus sign)

+ (repeats options)

FRAC Std.

FRAC COnSt

FRAC Std.

Note: Press o at any time to exit the Preference Mode. To Reset your calculator to the default Preference Settings, turn off your calculator, hold down the multiplication x key, and turn on. “ALL rESEt” will flash for one second before clearing the display.

APPENDIX H — CARE INSTRUCTIONS

Please follow the guidelines listed in this section for proper care and operation of your calculator. Not following the instructions listed below may result in damage not covered by your warranty. Refer to the Repair and Return section on page 116 for more details.

Do not expose calculator to temperatures outside the operating temperature range of 32ºF – 104ºF (0ºC – 40ºC).

Do not expose calculator to high moisture such as submersion in water, heavy rain, etc.

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APPENDIX I — ACCURACY, AUTO SHUT-OFF,

BATTERIES, ERRORS

Accuracy/Errors

Accuracy/Display Capacity — Your calculator has a twelve-digit display made up of eight digits (normal display) and four fractional digits. You may enter or calculate values up to 19,999,999.99. Each calculation is carried out internally to ten digits.

Errors — When an incorrect entry is made, or the answer is beyond the range of the calculator, it will display the word “ERROR.” To clear an error condition you must hit the o button once. At this point you must determine what caused the error and re-key the problem.

Error Codes:

Display

0-fL0

EXP Error

DIV Error

DIM Error

ENT Error

TYP Error

TRIG Error

None

Error Type

Overflow (too large to display)

Exponent Error

Divide by 0 Error

Dimension error

Entry error

Type error

Trig. error (for example, tan of 1 foot)

Attempt to calculate stairs without entering rise or run

Auto-Range — If an “overflow” is created because of an input and calculation with small units that are out of the standard range of the display (e.g. 19,999,999.99), the answer will be automatically expressed in the next larger units (instead of showing “ ERROR ”) — e.g., 20,000,000 mm is shown as 20,000 m. Also applies to inches, feet and yards.

Note: If Exponential Notation is activated through the Preference Setting, the value will be shown in scientific notation (e.g., 100 million mm—1.000000

8 mm).

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Auto Shut-Off

Your calculator is designed to shut itself off after about 8-12 Minutes of non-use.

Battery(ies)

• Two LR44 batteries.

Replacing the Battery(ies)

Should your calculator display become very dim or erratic, replace the battery(ies).

Note: Please use caution when disposing of your old battery, as it contains hazardous chemicals.

Replacement batteries are available at most discount or electronics stores. You may also call Calculated Industries at 1-775-885-4975.

Battery Replacement Instructions

To replace the batteries, slide open the battery door (at top backside of unit) and replace with new batteries. Make sure the batteries are facing positive side up.

Reset Key

If your calculator should ever “lock up,” press Reset — a small hole located to the left of the O key — to perform a total reset.

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REPAIR AND RETURN

WARRANTY, REPAIR AND RETURN INFORMATION

Return Guidelines

1.

Please read the Warranty in this User's Guide to determine if your ITI Sheet Metal/HVAC Pro calculator remains under warranty before calling or returning any device for evaluation or repairs.

2.

If your calculator won't turn on, try pressing the Reset button first. If it still won't turn on, check the batteries as outlined in the

User's Guide.

3.

If there is a black spot on the LCD screen, THIS IS NOT A

WARRANTY DEFECT. The unit can be repaired. Call for a repair quote before returning your unit.

4.

If you need more assistance, please contact the dealer through which you initially purchased the product. Or, contact the

International Training Institute at 1-703-739-7200.

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WARRANTY

Warranty Repair Service – U.S.A.

Calculated Industries (“CI”) warrants this product against defects in materials and workmanship for a period of one (1) year from the date of original consumer purchase in the U.S. If a defect exists during the warranty period,

CI at its option will either repair (using new or remanufactured parts) or replace (with a new or remanufactured calculator) the product at no charge.

THE WARRANTY WILL NOT APPLY TO THE PRODUCT IF IT HAS BEEN

DAMAGED BY MISUSE, ALTERATION, ACCIDENT, IMPROPER HAN-

DLING OR OPERATION, OR IF UNAUTHORIZED REPAIRS ARE

ATTEMPTED OR MADE. SOME EXAMPLES OF DAMAGES NOT COV-

ERED BY WARRANTY INCLUDE, BUT ARE NOT LIMITED TO, BATTERY

LEAKAGE, BENDING, OR VISIBLE CRACKING OF THE LCD, WHICH ARE

PRESUMED TO BE DAMAGES RESULTING FROM MISUSE OR ABUSE.

To obtain warranty service in the U.S., please contact the dealer through which you initially purchased the product.

A repaired or replacement product assumes the remaining warranty of the original product or 90 days, whichever is longer.

Non-Warranty Repair Service – U.S.A.

Non-warranty repair covers service beyond the warranty period or service requested due to damage resulting from misuse or abuse.

Contact Calculated Industries at 1-775-885-4900, to obtain current product repair information and charges. Repairs are guaranteed for 90 days.

Repair Service – Outside the U.S.A.

To obtain warranty or non-warranty repair service for goods purchased outside the U.S., contact the dealer through which you initially purchased the product. If you cannot reasonably have the product repaired in your area, you may contact CI to obtain current product repair information and charges, including freight and duties.

Disclaimer

CI MAKES NO WARRANTY OR REPRESENTATION, EITHER EXPRESS

OR IMPLIED, WITH RESPECT TO THE PRODUCT’S QUALITY, PER-

FORMANCE, MERCHANTABILITY, OR FITNESS FOR A PARTICULAR

PURPOSE. AS A RESULT, THIS PRODUCT, INCLUDING BUT NOT LIMIT-

ED TO, KEYSTROKE PROCEDURES, MATHEMATICAL ACCURACY AND

PREPROGRAMMED MATERIAL, IS SOLD “AS IS,” AND YOU THE PUR-

CHASER ASSUME THE ENTIRE RISK AS TO ITS QUALITY AND PER-

FORMANCE.

IN NO EVENT WILL CI BE LIABLE FOR DIRECT, INDIRECT, SPECIAL,

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INCIDENTAL, OR CONSEQUENTIAL DAMAGES RESULTING FROM ANY

DEFECT IN THE PRODUCT OR ITS DOCUMENTATION.

The warranty, disclaimer, and remedies set forth above are exclusive and replace all others, oral or written, expressed or implied. No CI dealer, agent, or employee is authorized to make any modification, extension, or addition to this warranty.

Some states do not allow the exclusion or limitation of implied warranties or liability for incidental or consequential damages, so the above limitation or exclusion may not apply to you. This warranty gives you specific rights, and you may also have other rights, which vary from state to state.

FCC Class B

This equipment has been certified to comply with the limits for a Class B computing device, pursuant to Subpart J of Part 15 of FCC rules.

Legal Notes

Licensed to International Training Institute by Calculated Industries 2006.

User’s Guide copyrighted by Calculated Industries, Inc., 2006.

Calculated Industries ® is a registered trademark of

Calculated Industries, Inc.

PATENT PENDING

ALL RIGHTS RESERVED

Designed in the U.S.A.

Looking For New Ideas

Calculated Industries, a leading manufacturer of special-function calculators and digital measuring instruments, is always looking for new product ideas in these areas.

If you have an idea, or a suggestion for improving this product or User’s

Guide, please submit your comments online at: www.calculated.com under

“Contact Us,” “Product Idea.” Thank you.

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INDEX

Accessing Preference Settings, 111

ACCURACY, AUTO SHUT-OFF, BATTERIES, ERRORS (APPENDIX I), 114

Accuracy/Errors, 114

Adding and Subtracting Fractions of an Inch, 35

Adding Dimensions, 29

Adding Linear Measurements, 34

Angle and Diagonal (Hypotenuse), 88

Arc Calculations — Arc Length and Diameter Known, 79

ARC/CIRCLE EXAMPLES, 78

Arched/Circular Rake-Walls — Chord Length and Segment Rise Known, 80

Arched Windows, 81

Arc Length — Degree and Diameter Known, 78

Arc Length — Degree and Radius Known, 78

AREA FORMULAS, 102

Area of a Rectangle, 36

Area of a Triangle, 37

AREA/VOLUME FORMULAS (APPENDIX B), 102

Auto Shut-Off, 115

Baluster Spacing, 100

BASIC EXAMPLES, 34

BASIC OPERATION KEYS, 6

Battery(ies), 115

Battery Replacement Instructions, 115

Calculating Angles Between Objects (“Angle Between”), 69

Calculating Angles Between Objects Example, 70

CARE INSTRUCTIONS (APPENDIX H), 113

Change OGEE Offset, 53

CIRCULAR/ARC FUNCTION KEYS, 15

Circumference and Area of a Circle, 36

Circumference of a Circle, 36

COLUMN/CONE KEY, 16

Common Rafter Length, 87

Common Rafter Length — Pitch Unknown, 87

CONCRETE/PAVING, 82

CONVERSIONS (LINEAR, AREA, VOLUME), 27

CONVERT Ç KEY—UNIT CONVERSIONS and SECOND FUNCTIONS, 6

Converting Decimal Feet to Feet-Inches-Fractions, 27

Converting Decimal Inches to Fractional Inches, 28

Converting Decimals to Fractions, 35

Converting degrees:minutes:seconds, 45

Converting Feet-Inches-Fractions to Decimal Feet, 27

Converting Feet-Inches to Meters and Millimeters, 34

Converting Feet-Inch-Fractions to Decimal Feet and Fractions of an Inch, 34

Converting FPM to Velocity Pressure, 47

Converting Fractional Inches to Decimal Inches, 27

Converting Fractions to Decimals, 35

Converting Pitch to Angle/Tangent, 45

Converting Velocity Pressure to FPM, 46

Cubed Function, 39

Cubed Root Function, 39

Cubic Conversions, 28

DEFAULT SETTINGS (APPENDIX F), 106

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Degree of Pitch, 86

Dividing Dimensions, 29

Dividing Offset into Multiple Degreed Elbows for Manageable Sections, 51

D:M:S EXAMPLE, 45

ENTERING DIMENSIONS, 25

Entering Linear Dimensions, 25

Entering Square/Cubic Dimensions, 25

EXAMPLES — USING THE SHEET METAL/HVAC PRO, 33

Fan Law 1, 75

Fan Law 2, 76

Fan Law 3, 77

FAN LAW EXAMPLES, 75

FAN LAW FORMULAS (APPENDIX E), 106

FAN LAW KEYS, 14

FEET-INCH-FRACTION and METRIC KEYS, 8

Field Measuring for Ductwork Using the Law of Cosines Introduction, 55

Finding “Angle A” (ArcSin, ArcCos, ArcTan), 41

Finding Length (of Iron) Required, 35

Finding Sine, Cosine, Tangent, 41

GETTING STARTED, 21

HIP/VALLEY and JACK RAFTER KEYS, 17

How to Set Preferences, 110

Inline Duct, Double Offset (Computing Offset, Length, and Angle), 62

Inline Duct, Single Offset (Computing Offset, Length, and Angle), 60

Irregular Hip/Valley and Jack Rafters — Descending, with On-Center Spacing

Maintained, 92

Jack Rafters — Using Other Than 16 Inch On-Center Spacing, 91

KEY DEFINITIONS, 6

LAW OF COSINES EXAMPLES, 55

LAW OF COSINES/HERON’S THEOREM FORMULAS (APPENDIX D), 105

LAW OF COSINES/NON-90 DEGREE TRIANGLE KEYS, 12

Linear Conversions, 27

MEMORY and STORAGE FUNCTIONS, 7

MEMORY OPERATION, 31

Multiplying Dimensions, 29

Non-90 Degree Triangle Measurement Using Law of Cosines and Heron’s

Theorem, 56

Objects at Right Angles, 65

Offset, Basic Example, 48

OFFSET EXAMPLES, 48

OFFSET FORMULAS (APPENDIX C), 104

OFFSET KEYS, 13

OGEE Offset in Feet-Inches-Fractions, 49

OGEE Offset, in Millimeters, 50

ORDER OF OPERATIONS, 21

Percentage Calculations, 30

Percent Grade, 86

PERFORMING BASIC MATH WITH DIMENSIONS, 29

PREFERENCE SETTINGS (APPENDIX G), 107

PYTHAGOREAN THEOREM/RIGHT TRIANGLE KEYS, 10

RECALL ® KEY, 8

Regular Hip/Valley and Jack Rafters, 89

REPAIR AND RETURN, 116

Replacing the Battery(ies), 115

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Reset Key, 115

RIGHT TRIANGLE and ROOF FRAMING EXAMPLES, 84

Rise, 88

Rise and Diagonal, 88

Roof Framing Definitions, 84

Scientific Notation, 39

Setting Fixed/Constant Fractional Resolution, 24

SETTING FRACTIONAL RESOLUTION, 23

Setting Fraction Resolution to Other Than 16ths — Using the Preference Setting

Mode, 23

Sheathing Cut, 89

Sheet Metal Panels for an Irregular Hip Roof, 59

Square Area (x 2 ), 36

Square Conversions, 28

Squaring-up a Foundation, 82

STAIR KEY, 19

Stair Layout Definitions, 94

STAIR LAYOUT EXAMPLES, 94

Stairs — Given Only Floor-to-Floor Rise, 96

Stairs — Given Only the Run, 98

Stairs — Given Rise and Run, 99

Subtracting Dimensions, 29

SURFACE AREA/VOLUME FORMULAS, 103

TRIGONOMETRY FORMULAS (APPENDIX A), 101

TRIGONOMETRIC KEYS, 9

TRIGONOMETRIC FUNCTIONS, 40

Using ArcK to Calculate an Arc Length, 78

Using Law of Cosines and Pythagorean Theorem to Calculate Offset, Length, and Angle, 58

USING PARENTHESES, 22

Using Trigonometry to Find Unknown Angle or Side, 42

Using Trigonometry to Find Unknown Side, 41

VELOCITY PRESSURE/FPM KEYS, 15

VELOCITY PRESSURE/VELOCITY EXAMPLES, 46

Volume of a Cone, 38

Volume of a Cylinder, 38

Volume of a Rectangle, 82

Volume of a Rectangular Box, 37

Volume of a Rectangular Container, Converting to Cubic Meters, 37

Volume of Columns, 83

WARRANTY, 117

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Designed in the United States of America

Printed in China

10/09

UG4090E-C