The Volume Of A Sphere Calculator
A sphere is the only solid whose volume and surface area both follow from a single measurement. Measure the radius once and every other quantity is a formula away.
Volume of the sphere
33.5103
- Surface area
- 50.2655
- Diameter
- 4
- Circumference
- 12.5664
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
V = (4/3) x pi x r^3
- r
- Radius, the distance from the centre to the surface
- V
- Volume enclosed by the sphere
- A
- Surface area of the sphere
- pi
- The constant 3.141592653589793
How to check the result by hand
- 1
Find the radius
If you measured across the ball, halve that figure. A ball thirty centimetres wide has a radius of fifteen centimetres. Everything else in this method needs the radius, not the diameter.
- 2
Cube the radius
Multiply the radius by itself twice. For a radius of 2 that is 2 times 2 times 2, which is 8. Cubing is the step that makes volume grow faster than the radius does.
- 3
Multiply by pi and four thirds
Take the cubed radius, multiply by 3.141592653589793, then multiply by four thirds, which is the same as multiplying by four and dividing by three. For a radius of 2 this gives 33.510321638291124 cubic units.
- 4
Square the radius for the surface area
Multiply the radius by itself once, not twice. For a radius of 2 that is 4, and four pi times 4 is 50.26548245743669 square units. Using the cube here instead of the square is the most common slip.
- 5
Report the diameter and circumference too
Double the radius for the diameter and multiply the radius by two pi for the circumference. These are the figures a tape measure produces, so they make the answer easy to sanity-check against the object in front of you.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate The Volume Of A Sphere page.