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cube · box · cylinder · sphere · cone

Volume calculator

Pick a solid, enter its dimensions, and read the volume in cubic units and litres, with the surface area and the substituted formula.

Short answer: a cube of side 2 has a volume of 8 cubic units and a surface area of 24. A 1 × 2 × 3 box is 6, a cylinder of radius 1 and height 2 is 2π ≈ 6.28318531, and a sphere of radius 1 is 4.18879020.

Square units in, cubic units out

The shapes here are the ones with a closed formula. Anything irregular needs either a displacement measurement or a mesh, and this page does not pretend to integrate an arbitrary shape — the honest answer for a bucket that is not a cylinder is to measure the water.

Worked example

A cylindrical water tank with a 0.75 m radius and 1.2 m height: V = π × 0.5625 × 1.2 = 2.1206 m³, which is 2,120.6 litres. The surface area, 2π×0.75×(0.75+1.2) = 9.19 m², is what you need for the paint.

Volume questions

Which solids are covered?

Cube, rectangular box, cylinder, sphere and cone — the five that come up in school work and in real measurements. Each shows its volume and surface-area formula and the substituted numbers.

How do cubic units convert to litres?

One cubic metre is exactly 1,000 litres, so 0.1 × 0.1 × 0.1 m is 0.001 m³ and therefore 1 litre. The page shows both, because tank and container sizes are usually quoted in litres.

What is the difference between volume and capacity?

Numerically nothing, but capacity is the internal space, so it uses internal dimensions and wall thickness matters. This page computes from the dimensions you give, so enter internal measurements for a capacity.

Why is the sphere formula 4/3 πr³?

Because a sphere fills two-thirds of the cylinder that just contains it, and that cylinder is πr² × 2r = 2πr³; two-thirds of that is 4/3 πr³. Its surface area, 4πr², is exactly the area of four of its great circles.

Related tools

Area calculatorThe two-dimensional shapes first.Density calculatorVolume plus density gives mass.Unit converterLitres, gallons and cubic metres.