Figure

Roof and stairs

Roof pitch

Enter or compare pitch in inches per foot, degrees, percent grade, and slope, then find related dimensions.1

Pitch per foot, degrees, percent grade and rise/run ratio describe the same slope in different forms. Distinguish horizontal run from full roof span and from the sloping rafter length.

An 8/12 pitch means 8 inches of rise for every 12 inches of horizontal run. Its rise/run ratio is 8 ÷ 12, its percent grade is that ratio × 100, and its angle above horizontal is inverse tangent of that ratio.

For 8/12, those forms are approximately 0.6667, 66.67% and 33.69°. With a known run, rise = run × pitch ÷ 12 when pitch is stated in inches per foot. Keep rise and run in matching units; a pitch angle is entered in degrees rather than labeled as a length.

Pitch in inches per foot

For an 8/12 pitch, enter 8 inches. Use your rise per 12 inches of run.

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.

Open Right

Skip if Right is already open. Skip Close if no mode is open.

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

Enter and calculate

  1. Inches of rise per foot

    Press 8, then inches, then Store pitch.

  2. Complete the value

    Press Equals.

Results in orderPress = to continue

  1. Pitch8 inches
  2. Angle33.69007°
  3. Percent grade66.66667
  4. Slope ratio0.6666667
  5. Pitch again8 inches

Keep in mind

Rounded measurements retain their underlying value unless the workflow explicitly rounds a stair step.

Pitch in degrees

Enter the angle in degrees without a length unit.

Start a new calculation

  1. Press Clear entry, then Clear entry.

Open Right

Skip if Right is already open. Skip Close if no mode is open.

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

Enter and calculate

  1. Angle in degrees

    Press 30.45, then Store pitch.

  2. Complete the value

    Press Equals.

Results in orderPress = to continue

  1. Angle30.45°
  2. Percent grade58.78702
  3. Slope ratio0.5878702
  4. Pitch per foot7 and 1/16 inches
  5. Angle again30.45°

Keep in mind

Rounded measurements retain their underlying value unless the workflow explicitly rounds a stair step.

Pitch as percent grade

Label percent with %, then tap Pitch.

Start a new calculation

  1. Press Clear entry, then Clear entry.

Open Right

Skip if Right is already open. Skip Close if no mode is open.

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

Enter and calculate

  1. Percent grade

    Press 47.25, then Second, then Percent, then Store pitch.

  2. Read percent grade

    Press Equals.

Results in orderPress = to continue

  1. Percent grade47.25
  2. Slope ratio0.4725
  3. Pitch per foot5 and 11/16 inches
  4. Angle25.29073°
  5. Percent grade again47.25

Keep in mind

Rounded measurements retain their underlying value unless the workflow explicitly rounds a stair step.

Find rise from pitch and run

Use pitch and horizontal run. Roof run is half-span only for a symmetric roof.

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.

Open Right

Skip if Right is already open. Skip Close if no mode is open.

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

Enter and calculate

  1. Inches of rise per foot

    Press 7, then inches, then Store pitch.

  2. Run

    Press 11, then feet, then 6, then inches, then Store run.

  3. Complete the value

    Press Equals.
  1. Example result6 feet 8 and 1/2 inches

Keep in mind

Pitch is saved between calculations. C → C clears the triangle but keeps that pitch; each worked example sets its own pitch or supplies both legs.

Find rise and diagonal from an angle

Use the angle in degrees and horizontal run.

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.

Open Right

Skip if Right is already open. Skip Close if no mode is open.

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

Enter and calculate

  1. Angle in degrees

    Press 30, then Store pitch.

  2. Run

    Press 20, then feet, then 4, then inches, then Store run.

  3. Complete the value

    Press Equals.
  1. Example · Rise11 feet 8 and 7/8 inches

Read the diagonal

  1. Press Equals.
  1. Example · Diagonal23 feet 5 and 3/4 inches

Keep in mind

Rounded measurements retain their underlying value unless the workflow explicitly rounds a stair step.

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 →