Figure

Shapes and geometry

Arcs

Relate circle size, arc length, and central angle and calculate arc length manually.

An arc is part of a circle’s curved edge. Its central angle describes how much of the circle it spans. Arc length follows the curve; the chord is the straight line between its endpoints.

Angle and diameter known

Use diameter and arc angle. Enter the angle without a length unit.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. Diameter

    Press 5, then feet, then Store diameter.

  2. Angle in degrees

    Press 85, then Store arc.

  3. Complete the value

    Press Equals.

Results in orderPress = to continue

  1. Arc length3 feet 8 and 1/2 inches
  2. Chord3 feet 4 and 9/16 inches
  3. Segment rise0 feet 7 and 7/8 inches
  4. Segment area1.522922 square feet
  5. Sector area4.636031 square feet
  6. Radius2 feet 6 inches
  7. Circumference15 feet 8 and 1/2 inches
  8. Circle area19.63495 square feet
  9. Arc length again3 feet 8 and 1/2 inches

Keep in mind

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

Angle and radius known

Use radius and arc angle. Tap Radius for half the width.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. Radius

    Press 24, then inches, then Store radius.

  2. Angle in degrees

    Press 77, then Store arc.

  3. Complete the value

    Press Equals.

Results in orderPress = to continue

  1. Arc length32 and 1/4 inches
  2. Chord29 and 7/8 inches
  3. Segment rise5 and 3/16 inches
  4. Segment area106.4256 square inches
  5. Sector area387.0442 square inches
  6. Diameter48 inches
  7. Circumference150 and 13/16 inches
  8. Circle area1809.557 square inches
  9. Arc length again32 and 1/4 inches

Keep in mind

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

Arc length and diameter known

Use diameter and measured arc length.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. Diameter

    Press 5, then feet, then Store diameter.

  2. Arc length

    Press 3, then feet, then 3, then inches, then Store arc.

  3. Complete the value

    Press Equals.

Results in orderPress = to continue

  1. Arc angle74.48451°
  2. Chord3 feet 0 and 5/16 inches
  3. Segment rise0 feet 6 and 1/8 inches
  4. Segment area1.051381 square feet
  5. Sector area4.0625 square feet
  6. Radius2 feet 6 inches
  7. Circumference15 feet 8 and 1/2 inches
  8. Circle area19.63495 square feet
  9. Arc angle again74.48451°

Keep in mind

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

Calculate arc length manually

Multiply angle in degrees by radius and π, then divide by 180.3

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

  1. Angle in degrees

    Press 100, then Multiply.

  2. Radius

    Press 5, then feet, then Multiply.

  3. Enter pi

    Press Second, then Pi.

  4. Divide

    Press Divide.

  5. Enter 180

    Press 180, then Equals.
  1. Example result8 feet 8 and 3/4 inches

Display assumptions

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

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

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

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 →