How sphere volume is calculated
A sphere's volume depends only on its radius, cubed.
V = 4/3 × π × r³ · A = 4 × π × r²
- If you measured the diameter, halve it to get the radius r.
- Cube the radius: r × r × r.
- Multiply by π (about 3.14159), then by 4/3. That is the volume in cubic units.
- Surface area is 4 × π × r², the area of four circles of the same radius.
- For litres: 1,000 cm³ is 1 litre and 1 m³ is 1,000 litres.
Worked example — A ball with a 5 cm radius: 5³ = 125, then 4/3 × π × 125 = 523.6 cm³, about 0.52 litres. Its surface area is 4 × π × 25 = 314.16 cm².
Common sphere sizes
| Diameter | Measured in | Volume | Litres | Surface area |
|---|---|---|---|---|
| 4 cm | Centimetres | 33.51 cm³ | 0.0335 L | 50.27 cm² |
| 6.7 cm | Centimetres | 157.48 cm³ | 0.1575 L | 141.03 cm² |
| 22 cm | Centimetres | 5,575.28 cm³ | 5.5753 L | 1,520.53 cm² |
| 24 cm | Centimetres | 7,238.23 cm³ | 7.2382 L | 1,809.56 cm² |
| 1 m | Metres | 0.52 m³ | 523.5988 L | 3.14 m² |
Swipe the table sideways to see the rest.
Diameters are approximate sizes of familiar balls.
Things to consider
- Measure the widest point across the ball for the diameter.
- Doubling the radius makes the volume eight times bigger.
- For a hemisphere, halve the volume.
- For a hollow ball, work out the outside and inside volumes and subtract.
Frequently asked questions
What is the formula for the volume of a sphere?
V = 4/3 π r³. Cube the radius, multiply by π, then by 4/3.
How do I use the diameter?
Choose Diameter and enter it. The calculator halves it to get the radius.
What is the surface area of a sphere?
A = 4 π r². A sphere of radius 5 cm has a surface area of about 314.16 cm².
How many litres does a sphere hold?
Work out the volume in cm³ and divide by 1,000. A 5 cm radius sphere holds about 0.52 litres.
Results are estimates for general information only, not financial, medical or professional advice.