Volume Calculator
Calculate volumes for standard 3D geometric shapes.
V = l × w × h
Cubes, cones, and the factor of three
Volume measures space in cubic units. Anything with a constant cross-section isbase area × height — which covers cubes, boxes, cylinders and every prism in one rule. Compute the area of the end and multiply by the length.
Solids that taper to a point take one third of that. A cone is ⅓πr²h and a pyramid is⅓ × base area × height. The one-third is not arbitrary: three identical pyramids of matching base and height fill their enclosing prism exactly, which is straightforward to demonstrate physically. A sphere is ⁴⁄₃πr³, which sits at two thirds of the cylinder that just contains it — a result Archimedes valued enough to have carved on his tomb.
Cubic units scale by the cube of the length factor, so 1 m³ is 1,000,000 cm³. Doubling every dimension multiplies volume by eight while surface area only quadruples — the reason bulk shipping is efficient and a large casserole takes far longer to cool than a small one. For capacity, 1 litre is exactly 1000 cm³.
Frequently Asked Questions
What is the volume formula for a cuboid?
Volume = length × width × height (l × w × h).
What is the volume formula for a cylinder?
Volume = π × r² × h, where r is radius and h is height.
What are the volume formulas for common solids?
Cuboid l × w × h; Cube a³; cylinder π × r² × h; sphere (4/3) × π × r³; cone (1/3) × π × r² × h.
How do I convert between volume units?
Cube the linear factor: 1 metre is 100 cm, but 1 cubic metre is 1,000,000 cubic centimetres. One litre is 1,000 cm³, one US gallon is about 3.785 litres, and one cubic foot is about 28.32 litres.