About the Sphere Calculator
A sphere is a perfectly round solid in which every point on the surface is the same distance from the centre. That distance is the radius, and everything else about the sphere follows from it. This calculator lets you start from whichever measurement you have: the radius, diameter, great-circle circumference, surface area or volume. It then works out the other four. It is handy for balls, tanks, domes, planets, ball bearings and school geometry questions, and it works with any unit of length as long as you stay consistent.
Updated October 2026
How to use the Sphere Calculator
- 1Choose the measurement you already know from the drop-down list.
- 2Type its value in the box.
- 3The calculator finds the radius first, then every other measurement.
- 4Read the volume and surface area in the result and the table.
- 5Remember that areas are in square units and volumes in cubic units.
A worked example
Suppose a football has a circumference of 68 cm around the middle. The radius is 68 divided by two pi, about 10.82 cm. The volume is then 4/3 × π × 10.82³, around 5,306 cubic centimetres, which is roughly 5.3 litres, and the surface area is about 1,471 square centimetres.
Spheres appear well beyond school problems. A brewer working out the capacity of a spherical fermenter, an engineer sizing a pressure vessel, a chef portioning round dumplings and a game designer scaling a planet all start from the same two formulas. Because volume grows with the cube of the radius, a small error in measuring the radius becomes a much larger error in volume: a 5 percent mistake in radius means roughly a 16 percent mistake in volume. Measure carefully and keep extra digits until the end.
Handy facts
- Doubling the radius multiplies the surface area by 4 and the volume by 8.
- Of all solids with the same volume, the sphere has the smallest surface area.
- A sphere that just fits inside a cube of side s takes up about 52 percent of the cube.
- Earth's mean radius is about 6,371 km, which gives a volume near 1.08 trillion cubic kilometres.
Related solids
For other shapes use the Cylinder Calculator, the Cone Calculator, the Volume Calculator and the Surface Area Calculator. The Circle Calculator handles flat circles, and the Concrete Calculator and Paint Calculator turn volumes and areas into material amounts.
Features
- Start from radius, diameter, circumference, area or volume
- Gives all five measurements at once
- Uses full-precision pi
- Works in any unit
- Refuses zero and negative values
- Copy button for the full result
Frequently asked questions
What is the formula for the volume of a sphere?
Volume equals four thirds times pi times the radius cubed. A ball with a radius of 3 cm has a volume of 4/3 × π × 27, about 113.1 cubic centimetres.
What is the surface area of a sphere?
Four times pi times the radius squared. The same ball with a 3 cm radius has a surface area of 4 × π × 9, about 113.1 square centimetres. Curiously, for a radius of 3 the area and volume have the same number.
How do I find the radius from the volume?
Multiply the volume by three, divide by four pi and take the cube root. The calculator does this when you pick volume as the known value, and then lists all the other measurements.
What is the circumference of a sphere?
A sphere has no single circumference, but the great circle around its widest point is 2 times pi times the radius. This is the measurement you get when you wrap a tape around the middle of a ball.
Can I convert the volume to litres?
Yes. If the radius is in decimetres, the volume in cubic decimetres is already in litres. If it is in centimetres, divide cubic centimetres by 1,000 to get litres. The Unit Converter and Volume Calculator can help with other units.
How is a hemisphere different?
A hemisphere is half a sphere. Its volume is half the sphere's volume. Its curved surface is half the sphere's area, and it adds a flat circular face of area pi r squared if you count the base.