Cube Volume Calculator

The volume of a cube is V = a³, where a is the length of one edge. Every edge is the same, so one measurement is all a cube needs. Enter it above and the calculator returns the volume with the working shown.

What the formula means

A cube is a box whose length, width and height are equal. The general box formula is length × width × height, and when all three are the same number that collapses to a × a × a, written a³. The word "cubed" for a third power comes directly from this shape.

Because the edge appears three times, the volume responds sharply to changes in it. Double the edge and the volume multiplies by eight. Halve the edge and it drops to an eighth. A cube twice as tall as another holds eight of it, which surprises people looking at two boxes side by side.

A worked example

Take an edge of 4 units.

• Multiply the edge by itself: 4 × 4 = 16
• Multiply by the edge again: 16 × 4 = 64 cubic units

Reversing it is just as useful. If you know the volume and want the edge, take the cube root. A cube holding 1000 cm³ has an edge of ∛1000 = 10 cm.

The one-metre cube

A cube one metre on each side has a volume of exactly one cubic metre, which is 1000 litres. That single fact anchors most practical volume estimates in metric units, because it lets you picture what a cubic metre actually is: roughly a washing machine, and a tonne of water.

The same trick works smaller. A cube 10 cm on each side is 1000 cm³, which is one litre. A cube 1 cm on each side is 1 cm³, which is one millilitre. The metric system was built around this relationship, which is why converting between volume and capacity needs no awkward constants.

Surface area alongside volume

A cube has six identical square faces, so its surface area is 6a². Volume rises with the cube of the edge while surface rises with the square, so the ratio of surface to volume falls as the cube grows. It works out at 6/a.

This is why sugar dissolves faster when ground, why a stack of small parcels costs more to wrap than one large one holding the same goods, and why storing anything in one large container loses less heat than storing it in many small ones.

Where it gets used

Shipping and storage. Volume determines what fits. A 20-foot shipping container has internal dimensions near 5.9 × 2.35 × 2.39 m, giving about 33.14 m³, and cargo is planned against that figure rather than against weight alone for bulky goods.

Materials. Concrete, soil, mulch and aggregate are sold by the cubic metre or cubic yard. Working out how many you need starts here, then adds an allowance for compaction and waste.

Packaging. Carriers charge on volumetric weight for light bulky items, calculated from the parcel's dimensions rather than the scales, so the box volume decides the price.

Crystallography and dice. Many crystals form cubic lattices, and the unit cell volume is the cube of the lattice constant. A standard die is a cube because a cube is the only shape with six identical faces that can be thrown fairly.

Units

Edge in	Volume in	Equivalent
1 cm	1 cm³	1 millilitre
10 cm	1000 cm³	1 litre
1 m	1 m³	1000 litres
1 ft	1 ft³	7.481 US gallons
1 yd	1 yd³	27 ft³

Note the last row. A cubic yard is 27 cubic feet rather than 3, because the factor of 3 applies to each of the three dimensions. This catches people ordering materials in yards and estimating in feet.

Turning volume into weight

Materials are ordered by volume and delivered by weight, so the conversion matters. Multiply the volume in cubic metres by the material's bulk density.

Material	Bulk density (t/m³)	One cubic metre weighs
Water	1.00	1.00 tonne
Dry sand	1.60	1.60 tonnes
Gravel	1.68	1.68 tonnes
Concrete	2.40	2.40 tonnes
Topsoil	1.30	1.30 tonnes

Bulk density counts the air between particles, which is why loose gravel weighs less per cubic metre than solid rock. It also rises with moisture, so wet sand is heavier than the table suggests and suppliers quote a range rather than a single figure.

Scaling, and why models mislead

Because volume follows the cube of length while area follows the square, scale models do not behave like the things they represent. A model at one tenth scale has a hundredth of the surface area and a thousandth of the volume, so it weighs a thousandth as much while its cross-sections are only a hundredth the size.

That mismatch is the square-cube law. It explains why an insect survives a fall that would kill a mouse, why very large animals need disproportionately thick legs, and why a scaled-up model of a working machine often cannot carry its own weight.

Cube roots in practice

Going backwards from volume to edge length comes up more often than expected. Sizing a cubic tank for a required capacity, finding the lattice constant of a crystal from its unit cell volume, or working out the edge of a box that holds a given number of litres all need the cube root.

A tank holding 2000 litres, which is 2 m³, needs an edge of the cube root of 2, about 1.26 m. Note how little the edge grows: doubling the capacity from 1000 to 2000 litres adds only 26 cm to each side. That is the square-cube law working in your favour for storage.

Stacking and usable space

Cubes stack perfectly, which is why boxes are rectangular rather than round. Unlike spheres, which waste about a quarter of any container, identical cubes fill a space completely when the container's dimensions are exact multiples of the edge.

In practice they rarely are. A 5.9 m container loaded with 0.4 m cubes fits 14 along its length with 0.3 m left over, so the usable fraction is 14 × 0.4 / 5.9, about 95%. Working out that remainder before ordering is what separates a load plan that works from one that leaves a pallet on the dock.

Diagonals

The longest straight line inside a cube runs corner to opposite corner and measures a√3, about 1.732 times the edge. A cube 1 m on each side has a space diagonal of 1.732 m.

This is the measurement that decides whether a long object fits in a box. A 1.7 m pole fits diagonally inside a 1 m cube even though every edge is shorter than the pole, which is a useful thing to know before cutting anything to length.

Common mistakes

Multiplying by three instead of cubing. An edge of 4 gives 64, not 12. Cubing means three factors multiplied, not multiplication by three.

Converting units after cubing rather than before. Convert the edge first. Converting a volume between systems needs the cube of the linear factor, which is where 27 comes from for yards to feet.

Assuming a box is a cube. If the three edges differ, it is a rectangular prism and needs all three measured.

Using external dimensions for capacity. Wall thickness reduces the usable interior, which matters for anything with substantial walls.