Volume of a Sphere: V = ⁴⁄₃πr³ With Examples
The volume of a sphere formula is V = ⁴⁄₃πr³. Cube the radius, multiply by π, then by 4 ⁄ 3.
3D Solids
Sphere
A sphere is the set of all points in space at distance r from the centre — a perfectly round ball.
- Volume
- V = (4 ⁄ 3) πr3
- Surface area
- SA = 4πr2
- r radius
Example 1: from the radius
A ball has a radius of 3 cm.
- V = ⁴⁄₃πr³
- V = ⁴⁄₃ × π × 3³ = ⁴⁄₃ × π × 27
- V = 113.1 cm³
Example 2: from the diameter
A basketball is 24 cm across.
- r = 24 ÷ 2 = 12 cm
- V = ⁴⁄₃ × π × 12³ = ⁴⁄₃ × π × 1,728
- V = 7,238.23 cm³ (about 7.2 litres)
Example 3: find the radius from the volume
A sphere holds 1,000 cm³. What is its radius?
- 1,000 = ⁴⁄₃πr³
- r³ = 1,000 × 3 ÷ (4π) = 238.73
- r = ∛238.73 = 6.2 cm
Why does r get cubed?
Volume uses three lengths, so the radius appears three times. Double the radius and the volume grows 2³ = 8 times.
Live calculator
Try the sphere calculator
Try it yourself
A marble has a radius of 1 cm. What is its volume?
Show the answer
V = ⁴⁄₃ × π × 1 = 4.19 cm³
Surface area is in our surface area of a sphere guide and on the sphere formulas page.
Volume of a sphere: FAQ
What is the volume of a sphere?
V = ⁴⁄₃πr³, where r is the radius.
How do I find the volume with the diameter?
Halve it to get the radius, or use V = πd³ ⁄ 6.
What happens to the volume if the radius doubles?
It becomes 8 times bigger, because 2³ = 8.