How to Use the Volume Calculator
Enter a radius and height to instantly calculate the volumes of all three common 3D shapes. The sphere only needs the radius; the cylinder and cone also need height.
- Sphere: V = (4/3) × π × r³
- Cylinder: V = π × r² × h
- Cone: V = (1/3) × π × r² × h
Fun fact: when h = 2r, the volumes of a cylinder, sphere, and cone with the same radius are exactly in the ratio 3 : 2 : 1 — a result Archimedes was proud of.
Frequently Asked Questions
Does the sphere need a height?
No. A sphere's volume depends only on its radius: V = (4/3)πr³. Height is used only for the cylinder and cone.
What unit is the result in?
The volume is in cubic units matching your input. Enter centimeters → cm³; enter feet → cubic feet.
Why is a cone's volume 1/3 of a cylinder's?
Mathematically proven: a cone with the same base and height fits exactly three times into a cylinder of the same dimensions.