Volume of a Cube Calculator

The volume of a cube formula

A cube is a solid with six identical square faces, so all twelve of its edges have the same length. Because length, width and height are equal, the box formula collapses to a single number multiplied by itself three times.

V = a × a × a = a³a is the length of one edge

Reading a³ aloud as "a cubed" is where the name of the operation comes from. The result is always in cubic units: an edge in centimeters gives cm³, an edge in feet gives ft³.

Calculating a cube's volume step by step

1. Measure one edge of the cube. Any edge will do, because they are all equal.
2. Enter it in Cube Side and select the unit next to it, from millimeters up to miles.
3. Press Calculate. The volume is shown with the unit cubed, for instance 27 cm³.

Whole-number volumes are shown without decimals. Others are shown with four decimals when that is enough, or six decimals when the exact value needs more, and large results use thousands separators.

Example: find the volume of a cube

Whole numbers. A cube with a 3 cm side has V = 3 × 3 × 3 = 27 cm³. A standard die measuring 16 mm along each edge has 16³ = 4,096 mm³, a little over 4 cm³.

Decimals. A planter box is a perfect cube with a 2.5 ft edge. The volume is 2.5³ = 15.625 ft³, which holds about 442 liters of soil. The calculator displays this as 15.6250 ft³, padding the result to four decimals.

Large cubes. A cube-shaped water tank 1 m on each side holds exactly 1 m³, which is 1,000 liters. The same tank measured as 100 cm per side has 100³ = 1,000,000 cm³, and each cubic unit is correspondingly smaller.

Cubes at a glance

Volume grows with the cube of the edge. Doubling the edge gives eight times the volume, while the surface area, 6a², only grows four times.

Cubic units and conversions

Changing the unit of the edge changes the volume by the cube of the conversion factor. A cube with a 1 m edge measures 100 cm along each side, so its volume is 100³ = 1,000,000 cm³, not 100 cm³. In the same way, a 1 ft cube is 12 in on a side and holds 12³ = 1,728 in³, and a 1 yd cube is 3 ft on a side and holds 27 ft³.

Liquid capacity links to cubes too. A 10 cm cube is 1,000 cm³, which is exactly one liter, and a 1 dm cube is the same thing by definition. Use the volume converter when you need to translate the answer into liters, gallons or other capacity units.

Finding the side from the volume

Reverse the formula with a cube root: a = ∛V. A cube that holds 343 cm³ has an edge of ∛343 = 7 cm. A cubic box that must hold 500 liters (0.5 m³) needs an edge of ∛0.5 ≈ 0.7937 m. The cube root calculator does this directly.

If the container is not a perfect cube, use the volume of a box calculator with three separate dimensions, or the volume calculator to mix units.

Common mistakes

• Multiplying by three instead of cubing. 3³ is 27, not 9. Cubing means three factors, not three times the number.
• Mixing up cubic and square units. Volume uses a³ and unit³, area uses a² and unit².
• Forgetting that the unit is cubed too. 1 m³ is 1,000,000 cm³, not 100 cm³, so converting between units needs the factor raised to the third power.
• Using an outside edge for capacity. For what a container can hold, use the inside measurement.

If you also need the outside area of the cube, try the surface area calculator.