Sphere Volume & Surface Area Calculator

About this calculator

A sphere’s volume, V = (4/3)πr³, and its surface area, A = 4πr², both derive entirely from the radius, and the two formulas are linked by a beautifully simple relationship first proven by Archimedes: a sphere’s volume equals exactly one-third of its radius times its surface area, and its volume and surface area are in the same 2:3 ratio as the cylinder that tightly circumscribes it — a result Archimedes considered his greatest achievement and reportedly asked to have carved on his tombstone.

These formulas turn up wherever a spherical shape needs to be sized or quantified: chemists and physicists use sphere volume to model atoms, droplets, or bubbles under the simplifying assumption of spherical geometry; engineers use surface area to compute heat transfer or coating material needed for ball bearings, tanks, and pressure vessels; and packaging and manufacturing use both figures together to determine material usage and storage capacity for anything from ball bearings to storage tanks.