Figure

Shapes and geometry

Right triangles

Find missing rise, run, or diagonal from two sides or a side and an angle.1

A right triangle has one 90° corner. Run, rise and diagonal describe its horizontal, vertical and sloping sides. Two compatible independent inputs determine the remaining sides and related angles.

For perpendicular run and rise, diagonal² = run² + rise². Use the same length unit for both legs before squaring. To find a missing leg instead, subtract the known leg’s square from the diagonal’s square, then take the square root.

The first example uses a 3 ft run and a 4 ft rise, giving √(3² + 4²) = 5 ft diagonally. The diagonal is the longest side. A measured shape must have a right angle for this relationship to apply.

Find the diagonal

Use the horizontal run and vertical rise.

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.

1. Enter Run

  1. Run

    Press 3, then feet, then Store run.

2. Enter Rise

  1. Rise

    Press 4, then feet, then Store rise.

3. Find the diagonal

  1. Press Equals.

Results in orderPress = to continue

  1. Example · Diagonal5 feet
  2. Run3 feet
  3. Rise4 feet
  4. Angle / plumb cutabout 53.13°
  5. Other angle / level cutabout 36.87°
  6. Pitch per 1216 inches
  7. Grade133.3333%
  8. Slope1.333333
  9. Back to diagonal5 feet

Read the angles

θ is the pitch angle; φ is the other acute angle. Together they make 90°. The selected angle is highlighted in the diagram and legend.

Change a value

Enter the new value, tap its input key, then =. Right Triangle keeps your two latest inputs. C keeps the setup; C twice clears it. Tap Close to leave the mode.

Find the run from rise and diagonal

Use the rise and diagonal.

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.

1. Enter Rise

  1. Rise

    Press 6, then inches, then 1, then Fraction, then 2, then Store rise.

2. Enter Diagonal

  1. Diagonal

    Press 12, then inches, then 1, then Fraction, then 16, then Store diagonal.

3. Find the run

  1. Press Equals.
  1. Example · Run10 and 3/16 inches

Find the rise from run and diagonal

Use the run and diagonal.

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.

1. Enter Run

  1. Run

    Press 3, then feet, then Store run.

2. Enter Diagonal

  1. Diagonal

    Press 5, then feet, then Store diagonal.

3. Find the rise

  1. Press Equals.
  1. Example · Rise4 feet

Find a transition's length

Use the offset and transition angle.

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.

Calculate

Skip Close if no mode is open.

  1. Press the keys

    Press Close calculation mode, then Open Right Triangle.

  2. Offset

    Press 18, then inches, then Store rise.

  3. Angle in degrees

    Press 20, then Store pitch.

  4. Complete the value

    Press Equals.
  1. Example result49 and 7/16 inches

Keep in mind

Right Triangle finds the missing side from a side and an angle.

Display assumptions

  1. Fraction precision: 1/16″; Fraction format: Simplified. ↩

References

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 →