Sphere Volume Calculator

Volume of a sphere formula

A sphere is fully described by one number, its radius, so a single formula covers every case.

V = (4 ÷ 3) × π × r³r is the radius, the distance from the centre to any point on the surface.

The radius is cubed, which means volume grows very quickly with size. A sphere with twice the radius holds eight times as much, and one with three times the radius holds 27 times as much.

If you know the diameter d instead, the same result can be written as V = π × d³ ÷ 6.

How to calculate the volume of a sphere

1. Find the radius. For a ball you measured across, divide the diameter by two.
2. Enter the radius in the box and pick its unit from the list next to it.
3. Press Calculate. The volume appears in the same unit cubed, rounded to six decimals.

No conversion happens between units, so a radius in centimetres gives a volume in cubic centimetres. To switch to litres, gallons or cubic feet afterwards, use the volume converter.

Example: find the volume of a sphere

A ball with a 3 cm radius. r³ = 27, so V = (4 ÷ 3) × π × 27 = 36π ≈ 113.097 cm³.

A water balloon, 24 cm across. The radius is 12 cm. V = (4 ÷ 3) × π × 12³ = (4 ÷ 3) × π × 1,728 ≈ 7,238.23 cm³, or a little over 7.2 litres. The shortcut with the diameter gives the same answer: π × 24³ ÷ 6 ≈ 7,238.23 cm³.

A planet. Earth's mean radius is about 6,371 km, so its volume is roughly (4 ÷ 3) × π × 6,371³ ≈ 1.083 × 10¹² km³. Choose kilometres in the unit list and the calculator gives the same figure.

A quick reference for small radii:

Finding the radius from the volume

To size a sphere for a given capacity, reverse the formula by taking a cube root.

r = ∛( 3 × V ÷ (4 × π) )

For example, a spherical tank that must hold 1 m³ needs r = ∛(3 ÷ (4π)) ≈ 0.620 m, which is a diameter of about 1.24 m. The cube root calculator helps with the last step.

How a sphere compares with other solids

Archimedes showed that a sphere takes up exactly two thirds of the smallest cylinder that can contain it (a cylinder as tall as the sphere is wide). With r = 5 cm the sphere holds about 523.6 cm³ and the cylinder around it about 785.4 cm³; the second figure comes from the cylinder volume calculator.

For the surface area as well as the volume, see the sphere calculator. The matching solids with a flat base are covered by the cone and cube volume calculators.

Where sphere volumes are used

Spherical shapes appear whenever a design needs the least surface for a given volume: pressure vessels, gas storage spheres, water towers, bubbles, droplets and ball bearings. Knowing the volume lets you work out capacity, and with a density it also gives the mass.

Example: a steel ball bearing is 10 mm across, so its radius is 5 mm and its volume is (4 ÷ 3) × π × 125 ≈ 523.6 mm³, or 0.5236 cm³. Steel weighs about 7.85 g per cm³, so the ball has a mass of roughly 0.5236 × 7.85 ≈ 4.11 g. The density calculator does that last step for any material.

Common mistakes

• Using the diameter as the radius. This makes the answer eight times too large.
• Forgetting to cube the radius, or squaring it by mistake. That mixes up area and volume.
• Mixing units, for example a radius in centimetres read as metres. The result changes by a factor of a million.
• Applying the formula to an egg or a flattened ball. The formula is only for a true sphere.