Figure

HVAC

Right angle duct offsets

Correct measured elevation slants before solving the plan triangle for ducts at right angles.1

This layout needs several linked calculations. Correct the elevation slants first, then use the resulting horizontal lengths in the plan triangle. Keep the same letter assignments and recorded precision through every stage.

Three stages to the plan dimensions

Correct the elevation slants first, then find the plan dimensions. Record results between stages.

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.

Elevation first

The elevation triangle uses θ = 90° − A and c as the diagonal.

Measured triangle: side a faces angle A, side b faces angle B, and side c faces angle C. Preserve these assignments when storing measurements.abcABC
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. Elevation side a

    Press 7, then feet, then 9, then inches, then 7, then Fraction, then 16, then Store side a.

Enter side b

  1. Elevation side b

    Press 2, then feet, then 2, then inches, then Store side b.

Enter side c

  1. Elevation side c

    Press 7, then feet, then 11, then inches, then 1, then Fraction, then 8, then Store side c.

  2. Press the keys

    Press Close calculation mode.

Find the pitch angle

Skip Close if no mode is open.

  1. Subtract angle A from 90°

    Press 90, 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.

Read the stored side

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.

2. Elevation offset Ye

  1. Press Equals.
  1. Example result1 foot 7 and 1/8 inches

Use = to select Rise.

3. Correct the first slant

  1. Press Equals.
  1. Example result7 feet 9 and 3/16 inches

Use = to select Run.

4. Correct the second slant

Use the recorded elevation offset from step 2. Match the transferred length precision to your work.

True-length right triangle: the slant measurement r is the hypotenuse, elevation offset y is perpendicular to the horizontal true length x. Find x from r and y.r · slantx · true lengthy
Schematic, not to scale.

  1. Start fresh

    Press Clear entry, then Clear entry.

  2. Second slant

    Press 11, then feet, then 8, then inches, then 13, then Fraction, then 16, then Store diagonal.

  3. Recorded elevation offset

    Press 1, then feet, then 7, then inches, then 1, then Fraction, then 8, then Store rise.

  4. Complete the value

    Press Equals.
  1. Example result11 feet 7 and 1/2 inches

5. Enter side a

Use the corrected horizontal sides for the plan triangle. Here θ = 180° − A.

  1. Start fresh

    Press Clear entry, then Clear entry.

  2. Press the keys

    Press Close calculation mode, then Open Oblique Triangle.

  3. Corrected plan side a

    Press 11, then feet, then 7, then inches, then 1, then Fraction, then 2, then Store side a.

Enter side b

  1. Plan side b

    Press 5, then feet, then 2, then inches, then Store side b.

Enter side c

  1. Corrected plan side c

    Press 7, then feet, then 9, then inches, then 3, then Fraction, then 16, then Store side c.

  2. Press the keys

    Press Close calculation mode.

Find 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.

Read the stored side

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.

6. Horizontal length Xp

  1. Press Equals.
  1. Example result4 feet 7 and 7/8 inches

Use = to select Run.

7. Horizontal offset Yp

  1. Press Equals.
  1. Example result6 feet 2 and 9/16 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 →