Figure

HVAC

Single duct offsets

Use measured triangle sides to find angle, offset, and length for the illustrated single-offset arrangements.1

A measured triangle establishes an angle and a sloping side; a corresponding right triangle separates that side into layout components. The letter assignments and angle conversion follow the particular sketch shown in the example.

Inline single offset

Match the measured setup below. Use the larger duct’s horizontal size as b.

Start a new calculation

Use 2nd if a unit is above its button.

  1. Start fresh

    Press Clear entry, then Clear entry.

  2. Press the keys

    Press Select length units.

Match the measured setup

For this orientation, θ = 180° − A. The right triangle uses c as its hypotenuse; x is the offset and y is the length along the ducts.

Measured triangle I and right triangle II share the slant side c. Angle A and Theta add to 180 degrees. In triangle II, x is beside Theta, y is opposite Theta, and the slant side is r.IIIAθabr = cxy
Schematic, not to scale.

1. Enter side a

Skip Close if no mode is open.

  1. Press the keys

    Press Close calculation mode, then Open Oblique Triangle.

  2. Side a

    Press 8, then feet, then 2, then inches, then 3, then Fraction, then 8, then Store side a.

Enter side b

  1. Side b

    Press 42, then inches, then Store side b.

Enter side c

  1. Side c

    Press 6, then feet, then 10, then inches, then Store side c.

  2. Press the keys

    Press Close calculation mode.

2. Find and assign the pitch angle

Skip Close if no mode is open.

  1. Subtract angle A from 180°

    Press 180, then Subtract, then Close calculation mode, then Open Oblique Triangle, then Close calculation mode.

  2. Complete the subtraction

    Press Equals.

  3. Open Right

    Press Close calculation mode, then Open Right Triangle.

  4. Assign Pitch

    Press Store pitch.
  1. Example result80.05446°

3. Use c as the diagonal

Skip Close if no mode is open.

  1. Press Close calculation mode, then Open Oblique Triangle.
  1. Example result6 feet 10 inches

Use = to select Side c.

Use c as the diagonal

Skip Close if no mode is open.

  1. Press the keys

    Press Close calculation mode.

  2. Complete the value

    Press Equals.

  3. Press the keys

    Press Close calculation mode, then Open Right Triangle.

  4. Press the keys

    Press Store diagonal.

4. Find offset x

  1. Press Equals.
  1. Example result1 foot 2 and 3/16 inches

Use = to select Run.

5. Find length y

  1. Press Equals.
  1. Example result6 feet 8 and 3/4 inches

Use = to select Rise.

Keep in mind

Keep the sides while switching modes. To use c again, open Oblique and press = until Side c is displayed. x/y names depend on your sketch's orientation; do not apply 180° − A to an unrelated setup.

Another measured-triangle example

Match the side letters to the diagram before storing measurements.

Start a new calculation

Use 2nd if a unit is above its button.

  1. Start fresh

    Press Clear entry, then Clear entry.

  2. Press the keys

    Press Select length units.

Match the side assignments

Measured triangle I and right triangle II share the slant side c. Angle A and Theta add to 180 degrees. In triangle II, x is beside Theta, y is opposite Theta, and the slant side is r.IIIAθabr = cxy
Schematic, not to scale.

1. Enter side a

Skip Close if no mode is open.

  1. Press the keys

    Press Close calculation mode, then Open Oblique Triangle.

  2. Side a

    Press 35, then feet, then 8, then inches, then 3, then Fraction, then 4, then Store side a.

Enter side b

  1. Side b

    Press 21, then feet, then 8, then inches, then 15, then Fraction, then 16, then Store side b.

Enter side c

  1. Side c

    Press 24, then feet, then 3, then inches, then 7, then Fraction, then 8, then Store side c.

  2. Press the keys

    Press Close calculation mode.

2. Calculate and assign the pitch angle

Skip Close if no mode is open.

  1. Subtract angle A from 180°

    Press 180, then Subtract, then Close calculation mode, then Open Oblique Triangle, then Close calculation mode.

  2. Complete the subtraction

    Press Equals.

  3. Open Right

    Press Close calculation mode, then Open Right Triangle.

  4. Assign Pitch

    Press Store pitch.
  1. Example result78.43128°

3. Read side c

Skip Close if no mode is open.

  1. Press Close calculation mode, then Open Oblique Triangle.

Use = to select Side c.

Use c as the diagonal

Skip Close if no mode is open.

  1. Press the keys

    Press Close calculation mode.

  2. Complete the value

    Press Equals.

  3. Press the keys

    Press Close calculation mode, then Open Right Triangle.

  4. Press the keys

    Press Store diagonal.

4. Find x

  1. Press Equals.
  1. Example result4 feet 10 and 9/16 inches

Use = to select Run.

5. Find y

  1. Press Equals.
  1. Example result23 feet 9 and 15/16 inches

Use = to select Rise.

Display assumptions

  1. Fraction precision: 1/16″; Fraction format: Simplified; Angle decimal places: Variable. ↩

Keep the guide beside your calculation.

These examples are built into Figure. Open Help while you calculate, then return to the same guide and reading position.

See Help in Figure →