A cube is one of the simplest shapes in geometry, and its volume is one of the simplest calculations in maths — you only need a single measurement. Dice, ice cubes, storage boxes and sugar cubes are all cubes, and once you know the cube volume formula, you can work out how much any of them holds in a few seconds. This article teaches the method by hand. If you only need the answer for a number in front of you, the Volume Calculator does it instantly.
What is a cube?
A cube is a three-dimensional shape with six square faces, twelve edges and eight corners. Every edge is the same length, so measure one edge and you know them all.
A die, a sugar cube, a storage box, an ice cube and a building block are all cubes. The key test is simple — if all three dimensions, length, width and height, are equal, the shape is a cube. If even one of them is different, it is a rectangular prism instead, a box with a different formula (more on that below). Because every edge is the same, a cube has only one measurement that matters: the side length, usually written as s.
The cube volume formula
The cube volume formula is:
V = s³
Volume equals the side length multiplied by itself three times: V = s × s × s. The little ³ is read as “cubed”, and it means exactly that — three copies of the side, multiplied together.
Take a cube with side 4: first 4 × 4 = 16, the area of one square face, then 16 × 4 = 64. So the volume is 64 cubic units — 4 × 4 × 4 = 64. Whatever the side length, the method is the same: side 5 gives 5 × 5 × 5 = 125 cubic units, side 10 gives 1,000, and side 2.5 gives 15.625 — decimals work exactly like whole numbers.
Why cubing the side gives cubic units
Volume measures space in three directions at once: length, width and height. Each multiplication in s × s × s accounts for one of those directions, and that is where the cubic units come from.
Picture a cube with side 4 cm filled with little 1 cm cubes. Along the bottom edge, 4 fit in a row; fill the whole bottom layer and you have 4 × 4 = 16 — the area of one face. Stack 4 layers high and 16 × 4 = 64 little cubes fill it completely: 64 cm³.
That is why the unit is cubed too: a length is measured in centimetres (cm), an area in square centimetres (cm²), and a volume in cubic centimetres (cm³). The same holds for any unit — metres give m³, inches in³, feet ft³. Always write the unit cubed: a volume of “64 cm” is a length, not a volume, and an exam marker will count it wrong.
Worked examples
A die, side 2 cm. A standard die is about 2 cm on each edge: volume = 2 × 2 × 2 = 8 cm³.
A storage cube, side 3 ft. Fabric storage cubes are often 3 ft on a side: volume = 3 × 3 × 3 = 27 ft³.
An ice cube, side 1.5 in. A large ice cube might be 1.5 inches on a side: volume = 1.5 × 1.5 × 1.5 = 3.375 in³ (1.5 × 1.5 = 2.25, then 2.25 × 1.5 = 3.375).
Sides 5 and 10. Side 5 gives 5 × 5 × 5 = 125 cubic units (5 × 5 = 25, then 25 × 5 = 125). Side 10 gives 10 × 10 × 10 = 1,000 — and a 10 cm cube holds exactly 1,000 cm³, which is exactly 1 litre.
Doubling the side. A cube of side 4 has volume 64; double the side to 8 and the volume becomes 8 × 8 × 8 = 512 — eight times bigger, not twice as big, because doubling every edge multiplies the volume by 2 × 2 × 2 = 8.
A cube is a special rectangular prism
A rectangular prism — an ordinary box — has volume V = l × w × h: length times width times height. A cube is simply the special case where all three sides are equal, so l = w = h = s, and the formula collapses to V = s × s × s = s³. Nothing changes in the maths; the cube formula is the box formula with all three numbers the same.
That gives you a handy cross-check: a box measuring 2 × 3 × 4 has volume 2 × 3 × 4 = 24 cubic units, while a 3 × 3 × 3 box has volume 27. If you ever forget the cube formula, fall back on the box formula and put the same number in three times.
Working backwards: from volume to side length
Sometimes you know the volume and need the side. A storage cube holds 64 cubic feet — how long is each edge? That is the reverse of cubing, called the cube root: find the number that, multiplied by itself three times, gives the volume.
For the neat numbers, test whole numbers: volume 64 → side 4, 27 → side 3, 125 → side 5, 216 → side 6, 1,000 → side 10, 8 → side 2. The small cubes are worth learning by heart: 1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125, 6³ = 216, 7³ = 343, 8³ = 512, 9³ = 729, 10³ = 1,000.
If it does not — say a volume of 100 — there is no whole-number side: the cube root of 100 is about 4.64, because 4.64³ is roughly 100, so use a calculator with a cube-root key. Working backwards also checks a forward answer: if a side-5 cube is 125 and the cube root of 125 brings you back to 5, the two directions agree.
Units and litres
Cube volumes often need converting into litres: 1,000 cubic centimetres equals 1 litre, so a 10 cm cube holds exactly 1 litre. A cube with side 0.5 m has volume 0.5 × 0.5 × 0.5 = 0.125 m³, and since 1 m³ is 1,000 litres, that is 125 litres. Convert the side first, then cube it.
Common mistakes
- Adding the sides instead of multiplying. A cube with side 4 does not have volume 4 + 4 + 4 = 12 — volume is a multiplication, three copies of the side multiplied together.
- Squaring instead of cubing. 4² = 16 is the area of one face, not the volume — one more multiplication by the side gives 16 × 4 = 64. Forgetting the third multiplication is the most common cube error.
- Mixing units. A 10 cm cube is 1,000 cm³, which is 1 litre — not 1,000 litres. Convert the side first, then cube it: a 0.5 m cube has volume 0.5 × 0.5 × 0.5 = 0.125 m³, which is 125 litres.
- Forgetting the cubic units. The number 64 on its own is not an answer — 64 cm³ is. Without the cubed unit, nobody can tell whether you mean a volume, an area or a length.
- Measuring the wrong side. Measure an edge, not a diagonal across a face — the face diagonal of a side-4 cube is about 5.66, and cubing that gives roughly 181 instead of 64.
Related tools
The Volume Calculator works out the volume of a cube from its side length — and also handles rectangular prisms, cylinders, cones, spheres and square pyramids — free, instant and with no sign-in. For all of ToolZana’s free tools, start at the ToolZana home page.
The short version
The cube volume formula is V = s³: multiply the side length by itself three times. Side 4 gives 4 × 4 × 4 = 64 cubic units, side 5 gives 125, side 10 gives 1,000, and a die with side 2 cm holds 8 cm³. The three multiplications are the three directions — length, width and height — which is why the answer is in cubic units (cm³, m³, in³). A cube is a rectangular prism with all three sides equal. To work backwards, take the cube root: volume 64 means side 4, volume 27 means side 3, volume 125 means side 5. Do not add the sides, do not stop at squaring, and always write the unit cubed.
Frequently Asked Questions
What is the cube volume formula?
The cube volume formula is V = s³, where s is the length of one side. Multiply the side by itself three times: V = s × s × s. For a cube with side 4, that is 4 × 4 × 4 = 64 cubic units. The side is the only measurement you need.
Why does cubing the side give cubic units?
Each multiplication in s × s × s accounts for one direction: length, width and height. A length is measured in centimetres, an area in square centimetres, and a volume in cubic centimetres. So a 4 cm cube has volume 64 cm³.
How do I find the volume of a cube with a side of 5 cm?
Multiply the side by itself three times: 5 × 5 × 5. First 5 × 5 = 25, the area of one square face, then 25 × 5 = 125. The volume is 125 cm³. The same steps work for any side length.
How do I work out the side length if I know the volume?
Take the cube root of the volume — the number that, multiplied by itself three times, gives the volume. Volume 64 means side 4, volume 27 means side 3, volume 125 means side 5, and volume 1,000 means side 10. For a volume like 100, the side is a decimal — about 4.64.
Is a cube the same as a rectangular prism?
A cube is a special kind of rectangular prism — the kind where all three sides are equal. A rectangular prism has volume V = l × w × h, and when l, w and h are all the same number s, that becomes V = s × s × s = s³. So every cube is a rectangular prism, but most rectangular prisms are not cubes.
How is the volume of a cube different from its surface area?
Volume is the space inside the cube, measured in cubic units; surface area is the skin outside it, measured in square units. A cube with side 4 has volume 4 × 4 × 4 = 64 cm³ but surface area 6 × 4² = 6 × 16 = 96 cm², because it has six square faces. Volume answers how much it holds; surface area answers how much material covers it, for example paint.
What happens if I square the side instead of cubing it?
You get the area of one face instead of the volume. For a cube with side 4, squaring gives 4² = 16 cm², one face; the volume is 16 × 4 = 64 cm³, one more multiplication by the side. Forgetting the third multiplication is the most common cube mistake.
Can I use decimals or fractions for the side length?
Yes — decimals work exactly like whole numbers in the cube volume formula. A cube with side 2.5 has volume 2.5 × 2.5 × 2.5 = 15.625 cubic units, and an ice cube with side 1.5 inches has volume 1.5 × 1.5 × 1.5 = 3.375 in³. A side of ½ is 0.5, and 0.5 × 0.5 × 0.5 = 0.125 cubic units.
How do I convert a cube volume to litres?
Use the fact that 1,000 cubic centimetres equals 1 litre. A cube with side 10 cm has volume 10 × 10 × 10 = 1,000 cm³, which is exactly 1 litre. A cube with side 0.5 m has volume 0.5 × 0.5 × 0.5 = 0.125 m³, and since 1 m³ is 1,000 litres, that is 125 litres.
What is the fastest way to check a cube volume?
Use the free Volume Calculator: pick the cube shape, type the side length, and it shows the volume with the formula and your numbers substituted in, so you can compare it with your hand calculation. It runs entirely in your browser.