Volume Calculator

Volume measures how much space a three-dimensional solid occupies, in cubic units. Most volume formulas are a base area multiplied by a height — cones and pyramids take exactly one third of their enclosing prism, a fact that surprises many people the first time they test it with sand or water.

Pick a solid and enter its dimensions: A is the side (cube), length (cuboid and pyramid base) or radius (sphere, cylinder and cone); B is the width or the height of the round solids; C is the remaining dimension for the cuboid and pyramid.

The formula

Cube a³ · Cuboid a×b×c · Sphere (4/3)πr³ · Cylinder πr²h · Cone (1/3)πr²h · Pyramid (a×b×h)÷3

Worked example

A cube with 3-unit edges holds 3 × 3 × 3 = 27 cubic units — the origin of the phrase 'cubed' for a third power.

The example is pre-loaded in the result panel — press Calculate with your own numbers to replace it.

Frequently asked questions

Why is a cone exactly one third of a cylinder?

A cone and cylinder with the same base and height always have volumes in the ratio 1:3 — fill a cone with water and it takes exactly three cones to fill the cylinder. Calculus proves it; the experiment is convincing on its own.

How do I convert cubic units to litres?

1 litre is exactly 1,000 cm³ (a cube 10 cm on each side). So calculate the volume in cubic centimetres and divide by 1,000 — a 30 × 20 × 15 cm box is 9,000 cm³ = 9 litres.

Category: Math calculators