About the Sphere Calculator
This sphere calculator works out every measurement of a ball from a single known value. Enter the radius, diameter, circumference, surface area or volume and it returns all the others, together with the volume and surface area of the matching hemisphere (half sphere).
It is useful for maths and physics homework, but also for everyday questions: how much air a ball holds, how much paint or leather covers a globe, how much concrete fills a dome, or what radius a spherical tank needs to hold a given volume. Working backwards from volume or surface area is where most people get stuck, so the calculator solves those directly.
Enter lengths in any unit; areas come out in square units and volumes in cubic units of the same kind. If you enter centimetres, the volume in cm³ is also millilitres, and dividing by 1,000 gives litres.
With the default inputs, the volume is 523.5988 cu units. Change any value above to recalculate instantly.
How to use the sphere calculator
- 1Choose which measurement you know — radius, diameter, circumference, surface area or volume.
- 2Enter the value.
- 3Read the volume, surface area and the remaining dimensions.
- 4Use the hemisphere results for domes, bowls and half-spheres.
Formula and method
A sphere is fully described by its radius r. Its volume is four-thirds π r³ and its surface area is 4πr² — exactly four times the area of a circle with the same radius. The diameter is 2r and the great-circle circumference (the widest loop around it) is 2πr.
To work backwards, the calculator inverts these: from a volume it takes the cube root of 3V ÷ 4π, and from a surface area it takes the square root of A ÷ 4π. A hemisphere has half the volume, (2/3)πr³, a curved surface of 2πr², and a total surface of 3πr² once the flat circular base (πr²) is included.
- r
- Radius
- V
- Volume
- A
- Surface area
- π
- Pi ≈ 3.14159
Worked examples
Sphere with a radius of 5
V = 4/3 × π × 125 ≈ 523.60 and A = 4 × π × 25 ≈ 314.16. A hemisphere of the same radius holds half, about 261.80.
Football with a 22 cm diameter
r = 11 cm, so V = 4/3 × π × 1,331 ≈ 5,575 cm³ — about 5.6 litres of air — and the cover is about 1,521 cm².
Radius of a 1,000-litre spherical tank
Working in decimetres (1 dm³ = 1 L), r = ∛(3 × 1,000 ÷ 4π) ≈ 6.20 dm, so the tank is about 1.24 m across.
Surface area of 100 square units
r = √(100 ÷ 4π) ≈ 2.821, which gives a volume of about 94.03 cubic units.
Frequently asked questions
What is the formula for the volume of a sphere?+
V = (4/3)πr³. For a radius of 3 the volume is 4/3 × π × 27 ≈ 113.1 cubic units.
How do I find the radius from the volume?+
Rearrange to r = ∛(3V ÷ 4π). Multiply the volume by 3, divide by 4π, then take the cube root. A volume of 1,000 gives r ≈ 6.20.
What is the surface area of a sphere?+
A = 4πr², which is four times the area of the sphere’s cross-sectional circle. A ball of radius 5 has a surface area of about 314.16.
How do you find the volume of a hemisphere?+
Halve the sphere volume: V = (2/3)πr³. Its total surface, including the flat base, is 3πr².
How do I convert the volume to litres?+
If you measured in centimetres, divide cubic centimetres by 1,000 to get litres. If you measured in metres, multiply cubic metres by 1,000. For inches, divide cubic inches by 231 for US gallons.