Figure

Shapes and geometry

Circular segments

Relate chord width, rise, radius, and arc measurements using an arched-window example.

A circular segment lies between a chord and its arc. Chord width and segment rise describe an opening such as an arched window. The rise starts at the chord and is different from the circle’s radius.

From chord and rise

Use chord width and rise from the chord to the top of the arc.1

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 Circle

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

  1. Press Close calculation mode, then Open Circle.

Enter and calculate

  1. Chord

    Press 2, then feet, then 7, then inches, then Store chord.

  2. Rise

    Press 10, then inches, then 1, then Fraction, then 2, then Store rise.

  3. Complete the value

    Press Equals.
  1. Example result16 and 11/16 inches

Keep in mind

Keep pressing = for the arc angle, curved length and areas. Entered measurements stay in the setup.

Read the window arc results

Use chord and rise, then read the arc outputs.2

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 Circle

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

  1. Press Close calculation mode, then Open Circle.

Enter and calculate

  1. Chord

    Press 2, then feet, then 7, then inches, then Store chord.

  2. Rise

    Press 10, then inches, then 1, then Fraction, then 2, then Store rise.

  3. Complete the value

    Press Equals.

  4. Complete the value

    Press Equals.

Results in orderPress = to continue

  1. Arc angle136.4579°
  2. Arc length39 and 3/4 inches
  3. Segment area235.7767 square inches
  4. Sector area331.729 square inches
  5. Diameter33 and 3/8 inches
  6. Circumference104 and 7/8 inches
  7. Circle area875.1597 square inches
  8. Radius16 and 11/16 inches
  9. Arc angle again136.4579°

Keep in mind

The displayed fractions are rounded; calculations retain the underlying value.

Radius and chord known

Use radius and chord width.3

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. Open Circle

    Press Close calculation mode, then Open Circle.

  2. Radius

    Press 5, then feet, then Store radius.

  3. Chord

    Press 6, then feet, then Store chord.

  4. Complete the value

    Press Equals.
  1. Example result1 foot 0 inches

Radius and rise known

Use radius and rise from chord to arc.3

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. Open Circle

    Press Close calculation mode, then Open Circle.

  2. Radius

    Press 5, then feet, then Store radius.

  3. Rise

    Press 1, then feet, then Store rise.

  4. Complete the value

    Press Equals.
  1. Example result6 feet 0 inches

Display assumptions

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

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

  3. Fraction format: Simplified. ↩1↩2

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 →