Cone Volume Calculator
A Third of a Cylinder
Take a cylinder and a cone that share the same circular base and the same height, and the cone always turns out to hold exactly one-third the volume — a relationship first proven geometrically by Eudoxus over two thousand years ago and still the cleanest way to remember the formula.
The Formula
Volume = (πr²h) / 3
Worked Example
For a cone with radius 3 and height 8 — the same dimensions as the cylinder example above:
| Shape | Formula | Volume |
|---|---|---|
| Cylinder (r=3, h=8) | πr²h | 226.1947 |
| Cone (r=3, h=8) | πr²h / 3 | 75.3982 |
75.3982 is exactly one-third of 226.1947, confirming the cylinder-to-cone relationship.
Where This Matters
- Hopper and silo design — the conical bottom section of a storage hopper holds material according to this formula.
- Volume of piles — sand, gravel, or grain heaped into a roughly conical mound can be estimated this way from its base radius and height.
- Funnels and nozzles — sizing the internal volume of conical flow components.
How to Use This Calculator
- Enter the cone's Radius.
- Enter the cone's Height.
- Select Calculate to get the volume.
Related Calculations
Compare against a full cylinder with the Cylinder Volume Calculator, or find the cone's curved surface with the Lateral Area Calculator.