Volume Of a Cube Calculator

What this calculator does

A cube is the perfectly even solid: six square faces, and every edge the same length. Because everything about it is equal, a single number settles its size, the length of one edge.

Type the edge, pick a unit, and the tool gives you the volume, the amount of space inside: a dice, a sugar cube, a cubic crate.

Using the calculator

1. Type the edge length.
2. Pick its unit.
3. Press Calculate.

There is one box, since all the edges of a cube are equal. The edge has to be positive, and the volume comes back in cubic units of the edge's unit.

The formula | volume = edge³

The volume of a cube is:

volume = edge × edge × edge = edge³

Multiply the edge by itself three times. This is the three-dimensional partner of squaring. A square's area is side × side, written side²; a cube's volume is side × side × side, written side³. And just as the square gives "squaring" its name, the cube gives "cubing" its.

Cubes and perfect cube numbers

If the edge is a whole number, the volume lands on the perfect cubes: 1, 8, 27, 64, 125, and on up. Each is the number of little unit cubes that pack a cube that many units along each edge, so a 4 by 4 by 4 cube holds 64 of them.

You can see the whole run in the cube numbers list.

Read another way: base area times height

There is a second way to look at edge³ that is worth knowing, because it connects the cube to every other box and tube. The bottom face is a square of area edge × edge, and the cube is that square raised straight up by the edge's height. So the volume is the base area times the height: (edge²) × edge, which is edge³.

That base-area-times-height idea is the same one behind the volume of any box, prism or cylinder. The cube is just its tidiest case.

Why the answer is in cubic units

Volume multiplies three lengths together, so it comes out in cubic units: centimetres times centimetres times centimetres give cubic centimetres, cm³. It is the three-dimensional cousin of area. Area multiplies two lengths and is squared; volume multiplies three and is cubed.

A worked example | a 10 cm edge

Say the edge is 10 cm.

1. Multiply it by itself three times: 10 × 10 × 10 = 1,000.

So the volume is 1,000 cm³. Picture it as 1,000 little one-centimetre cubes, stacked 10 layers high with 100 in each layer, filling the cube exactly.

A cube is a special box

A cube is the special case of a box, or rectangular prism, where the length, width and height happen to all be equal. The general formula is length × width × height, and when all three are the same edge, that becomes edge³. If your sides are not equal, the volume of box calculator or the rectangular prism calculator is the one to reach for.

Questions people ask

What is the volume of a cube with a 10 cm edge?

It is 1,000 cm³. Multiply the edge by itself three times: 10 × 10 × 10.

Why is it edge cubed?

Because a cube has three equal dimensions, and multiplying them gives edge × edge × edge, which is edge³. That is exactly what "cubing" a number means.

What is a perfect cube?

A whole number that is the volume of a cube with a whole-number edge, like 1, 8, 27 and 64. They come from multiplying a whole number by itself three times.

Why is the answer in cubic units?

Because volume multiplies three lengths. Edges in centimetres give a volume in cubic centimetres, cm³.

What is the difference between this and a box?

A cube has all edges equal, so it needs one measurement. A box, or rectangular prism, can have a different length, width and height, so it needs all three.

References

A note on where this comes from. The cube is one of the five Platonic solids, the regular ones with identical faces, known as the regular hexahedron and treated by Euclid in the Elements. Its volume, like that of any box, is the area of its base raised through its height. For further reading, see Cube.

1. Euclid, Elements, Book XIII (c. 300 BCE), on the cube (regular hexahedron) as one of the five Platonic solids.