Volume of a sphere

Sphere formulas

• Volume: V = 4/3 × π × r³
• Surface area: S = 4 × π × r²

Archimedes proved both in the 3rd century BC and was so proud of the result, that a sphere has two-thirds of the volume of the cylinder around it, that he asked for it to be carved on his tomb.

Worked examples

A ball with a 3 cm radius holds 4/3 × π × 27 ≈ 113.1 cm³ and has a surface of 4 × π × 9 ≈ 113.1 cm²: at r = 3 the two numbers coincide. A size-5 football, 22 cm across (r = 11 cm), holds about 5,575 cm³, roughly 5.6 litres of air.

Doubling the radius

Double the radius and the volume grows 8 times (2³) while the surface grows 4 times (2²). That is why large raindrops and planets behave so differently from small ones.

The page cubes the radius and multiplies by 4/3 π for the volume, and squares it and multiplies by 4π for the surface area, using π to full double precision. The diameter is twice the radius. Results carry your unit cubed for volume and squared for area. Everything runs in your browser.