The Sphere's Key Measures

From a single radius everything follows: diameter 2r, circumference 2πr, cross-section area πr², surface area 4πr², and volume 4/3πr³. Enter either the radius or diameter — the calculator derives the rest.

Archimedes' Masterpiece

Archimedes proved the sphere's surface area equals four great circles and its volume equals two-thirds of its circumscribed cylinder — the result he considered his greatest and asked to be carved on his tombstone. The donut chart above shows that exact 2:1 ratio with the cylinder's leftover space.

Why Spheres Matter

The sphere is the most efficient container — maximum volume for minimum surface — which is why drops, planets, and bubbles are spherical. Surface area governs cooling, evaporation, and drag, so both measures matter in engineering and physics.