Math and relationships

Cubes and cube roots

Cube numbers or measured lengths and recover a cube’s side from its volume.

A cube’s volume is side × side × side. Cubing a length produces cubic units, and cube root returns the side of a cube from its volume. Other shapes need their own volume relationship.

Find a cube’s volume or side

Use one side of a cube to find its volume, or its volume to find the side.1

Cube, then undo it

x³ multiplies a number by itself twice: 2 × 2 × 2 = 8. ³√x reverses that calculation. Press 2nd → x³ to cube, or 2nd → ³√x for cube root.

A cube with every side 2 meters long has a volume of 8 cubic meters. Cubing the side gives volume; cube root of volume gives the side.8 m³2 m
Schematic, not to scale.

Try it · a cube with 2 m sides

Use 2nd if m is above its key.

  1. Start fresh

    Press Clear entry, then Clear entry, then Select length units.
  2. Enter one side and cube it

    Press 2, then meters, then Second, then Cube.
  1. Volume8 cubic meters

Get the side back

  1. Take the cube root

    Press Second, then Cube root.
  1. Side length2.000 meters

Also useful for

Cube-shaped bins, boxes and forms. Cubing a scale ratio also tells you how volume changes when every dimension scales equally.

Remember

The side-from-volume shortcut works only for a cube. For a rectangular box, multiply length × width × height. Cube root is not volume ÷ 3.

Cube a number

Enter a number without units, then cube it.

Start a new calculation

  1. Press Clear entry, then Clear entry.

Calculate

  1. Number

    Press 10, then Second, then Cube.
  1. Example result1000

Cube a length

Cube a measured length to get volume.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.

Calculate

  1. Length

    Press 3, then meters, then Second, then Cube.
  1. Example result27 cubic meters

Cube root of a number

Enter a number without units, then find its cube root.

Start a new calculation

  1. Press Clear entry, then Clear entry.

Calculate

  1. Number

    Press 100, then Second, then Cube root.
  1. Example result4.641589

Cube root of a volume

Label the volume with cubic units before finding its cube root.2

Start a new calculation

  1. Press Clear entry, then Clear entry.

Calculate

  1. Volume

    Press 2028, then Select volume units, then Cubic inches, then Second, then Cube root.
  1. Example result12 and 11/16 inches

Display assumptions

  1. Volume units: Automatic. ↩1↩2

  2. 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 →