Sphere Volume Calculator
The formula
Volume = 4/3 × π × radius³
The result is in cubic units: a radius in centimetres gives cm³ (1,000 cm³ = 1 litre), a radius in metres gives m³ (1 m³ = 1,000 litres).
Worked examples
- A sphere with a 10 cm radius: 4/3 × π × 1,000 = 4,188.8 cm³, about 4.2 litres.
- A size-5 football, about 22 cm in diameter (radius 11 cm): 5,575 cm³, roughly 5.6 litres of air.
- The Earth (mean radius 6,371 km): about 1.08 × 10¹² km³, or 1,083 billion cubic kilometres.
Radius and volume: the cube effect
Because the radius is cubed, volume grows very fast:
| Radius multiplied by | Volume multiplied by |
|---|---|
| 2 | 8 |
| 3 | 27 |
| 10 | 1,000 |
A ball twice as wide holds eight times as much. Conversely, a balloon that holds 8 times more air is only twice as wide.
From diameter, circumference or volume
- From the diameter: halve it first, or use V = π × d³ ÷ 6.
- From the circumference C: r = C ÷ (2π). A ball measuring 70 cm around has a radius of 11.1 cm.
- Radius from volume: r = ∛(3V ÷ 4π). A 1-litre sphere (1,000 cm³) has a radius of 6.2 cm.
Surface area
The surface of a sphere is 4πr² — exactly four times the area of a circle of the same radius. For a 10 cm radius, 1,257 cm². A sphere encloses the largest volume for a given surface, which is why bubbles and water droplets are round and why spherical tanks are used for pressurised gas.
Hemispheres and domes
A hemisphere holds half the volume: 2/3 × π × r³. A hemispherical bowl 20 cm across (radius 10 cm) holds about 2.1 litres. Use the volume converter to express the result in gallons or cups.
Frequently Asked Questions
How do I convert the volume of a sphere to litres?
If the radius is in centimetres, divide the result in cm³ by 1,000. If it is in metres, multiply the result in m³ by 1,000.
How do I find the volume from the diameter?
Divide the diameter by 2 to get the radius, or use V = π × d³ ÷ 6 directly.
What is the formula for the surface area of a sphere?
4 × π × r². For a radius of 10 cm, the surface is about 1,257 cm².