What is the volume of a cube?
A cube is the 3D version of a square — six identical square faces joined together to form a solid. Every cube has just one number that defines it: the side length, usually written as s. Once you know s, you know everything about the cube, because every face is a square of that size and every edge is the same length.
The volume of a cube — how much space it occupies — is the side length cubed:
V = s³ = s × s × s
The "cubed" terminology literally comes from the cube. When you raise a number to the third power (s³), geometrically you're computing the volume of a cube of side s. The unit conventions follow the same rule: if s is in centimeters (cm), then V is in cubic centimeters (cm³). If s is in inches, V is in cubic inches (in³). Always cube the unit, not just the number.
How to use the cube volume calculator
Three steps:
- Enter the side length of the cube in the field. For example, type 5.
- The volume appears instantly: 5³ = 125.
- Below the volume you also get three other useful measurements: surface area, face diagonal, and space diagonal — all derived from the same side length.
Tap any worked example to load a real-world cube — a Rubik's cube, a 10 cm "1 litre" cube, a moving box — and watch the values update.
Worked examples
Example 1 — Unit cube (s = 1)
V = 1³ = 1. The unit cube is the building block of all volume — when mathematicians want to define what "1 unit of volume" means, they point to a 1×1×1 cube. Surface area = 6, face diagonal = √2 ≈ 1.414, space diagonal = √3 ≈ 1.732.
Example 2 — 10 cm cube → 1 litre
V = 10³ = 1000 cm³. By definition, 1 litre is exactly 1000 cm³, so a 10 cm × 10 cm × 10 cm cube holds precisely one litre of water (which weighs about 1 kilogram). This is one of the most useful unit conversions to memorize: any cube with sides of 10 cm has volume 1 L.
Example 3 — Moving box (30 cm cube)
V = 30³ = 27,000 cm³ = 27 L. A 30 cm cube — about the size of a small moving box or a microwave — has 27 litres of capacity. Notice the volume scales with the cube of the side length: tripling the side from 10 cm to 30 cm makes the box 27 times larger, not 3 times larger.
Example 4 — 1 metre cube
V = 100³ = 1,000,000 cm³ = 1 m³ = 1000 L. A cube one metre on a side holds a thousand litres — that's a huge volume. Industrial water tanks, large shipping pallets, and intermediate bulk containers (IBC totes) are typically rated in cubic metres for this reason.
Surface area, face diagonal, space diagonal
The calculator gives you three more measurements alongside volume — all derived from the same single input.
Surface area: 6s²
A cube has six identical square faces, each with area s². Total surface area is 6 × s². For a 5 cm cube: surface area = 6 × 25 = 150 cm². Surface area is what you'd need to know if you wanted to paint, wrap, or wallpaper the outside of the cube.
Face diagonal: s√2
Each face of the cube is a square. The diagonal across that square (corner to corner of one face) is s × √2 ≈ s × 1.414. This comes straight from the Pythagorean theorem: a square with side s has a diagonal of √(s² + s²) = s√2. For a 10 cm cube, the face diagonal is about 14.14 cm — the longest line you can draw on a single face without leaving it.
Space diagonal: s√3
The space diagonal goes through the interior of the cube, from one corner to the opposite corner — passing through the very centre of the solid. Its length is s × √3 ≈ s × 1.732. The proof is two applications of the Pythagorean theorem: first compute the face diagonal (s√2), then compute the diagonal of the rectangle formed by the face diagonal and the cube's height: √((s√2)² + s²) = √(3s²) = s√3. The space diagonal is always longer than the face diagonal, which is always longer than the side. For a 10 cm cube: side 10, face diagonal ≈ 14.14, space diagonal ≈ 17.32.
From volume back to side length
If you know the volume and want the side length, take the cube root: s = V^(1/3). For V = 27: s = ∛27 = 3. For V = 1000: s = ∛1000 = 10. Most scientific calculators have a cbrt() or x^(1/3) function; on a regular calculator you can compute V^(1/3) directly using the power button.
This inversion is useful when you have a volume requirement (a tank that needs to hold X litres, a box that must contain Y cubic feet) and you want to know how big the cube has to be. Need a 1000-litre tank? You need a cube with sides of (1,000,000)^(1/3) = 100 cm = 1 metre.
Why volume scales with the cube of the side
One of the most counterintuitive facts about cubes is how dramatically volume changes when you change the side length. Doubling s makes V eight times bigger. Tripling s makes V twenty-seven times bigger. Multiplying s by 10 makes V a thousand times bigger.
This is the cube-square law and it explains a lot of the world. Why are mice fluffy and elephants nearly hairless? Because heat loss happens through surface area (which grows with s²), and heat production happens through volume (which grows with s³). Bigger animals have proportionally less surface area per unit of body mass, so they need less insulation. Why do small bugs survive falls that would kill us? Same math — their tiny mass (volume × density) means low impact energy, but their surface area is large enough to slow them down through air resistance. Why are massive ships made of metal that floats while a tiny pebble sinks? Because hollow ship shapes have huge displacement (volume) relative to their material (which is the surface that bounds the volume).
Where cubes show up in everyday life
- Storage — moving boxes, shipping containers, dishwasher tablets, ice cubes. The cube is the most space-efficient regular shape for stacking, because identical cubes tile space with no gaps.
- Cooking — diced ingredients ("cut into 1-inch cubes"), bouillon cubes, sugar cubes, ice cubes. Recipes use cube measurements because cubes have predictable volume per side length.
- Architecture — modernist buildings often use cube-like volumes (the Apple Park glass cube on Fifth Avenue, brutalist housing blocks). The cube reads as deliberate, geometric, no-frills.
- Games — dice (six faces, identical squares), Rubik's cube (3³ = 27 mini-cubes), Minecraft (entire worlds built from 1m cubes). The cube is the simplest 3D shape to reason about, which is why it shows up so often in voxel-based games.
- Storage units — self-storage units are typically advertised by floor area (5×5, 10×10), but the volume calculation matters more for what fits inside. A 10 ft × 10 ft × 8 ft unit has 800 ft³ of space.
Common mistakes
- Squaring instead of cubing. Easy to slip up: s² gives surface-of-one-face, not the volume. The volume always uses the third power.
- Forgetting to cube the units. 5 cm cubed is 125 cm³, not 125 cm. Volume always carries cubic units (cm³, m³, in³, ft³).
- Confusing volume with surface area. A larger cube has more volume per surface area — both grow, but volume grows faster. Don't substitute one for the other when comparing how much fits inside vs how much you have to cover outside.
- Mixing up face diagonal and space diagonal. Face diagonal lives on one face; space diagonal goes through the interior. The space diagonal is always the longer one (s√3 vs s√2).
What the calculator gives you, summarized
From a single side length, you get four results:
- Volume — V = s³, the cube's interior capacity.
- Surface area — 6s², the total outer skin of the cube.
- Face diagonal — s√2, the diagonal across any single face.
- Space diagonal — s√3, the longest straight line that fits inside the cube.
One input, four outputs — all from the basic geometry of the cube.