Volume Calculator

Volume calculations come up anywhere something needs to fill, hold, or be poured into a 3D shape: how much concrete a cylindrical or box-shaped footing needs, how much water a spherical or cylindrical tank holds, how much a shipping box can fit, or a geometry student working through the formulas for cube, box, sphere, cylinder and cone. Every shape has its own formula, and this calculator covers the five that account for nearly every real-world volume question.

Beyond the raw number, seeing how these shapes relate to each other — a cone is always exactly a third of the cylinder that shares its base and height, a sphere is always exactly two-thirds of the cylinder that tightly wraps around it — is often the more useful takeaway, since it means you only really need to remember one formula and derive the others.

A cube's volume is side³ (the side length multiplied by itself three times), and a rectangular box generalizes that to length × width × height, for when the three dimensions differ. A cylinder's volume is πr²h — the circular base's area (πr²) extended along its height.

A cone's volume is exactly ⅓ × πr²h — one third of a cylinder sharing the same base and height, because a cone tapers to a point instead of keeping a constant cross-section all the way up. A sphere's volume is (4/3)πr³, and it works out to exactly two-thirds of the volume of the tightest-fitting cylinder around it (radius r, height 2r) — a classical result first proven by Archimedes.