How to use the Cone Volume Calculator
Enter the base radius and the vertical height in the same unit.
The cone volume formula
A cone holds exactly one third of a cylinder with the same base and height. Multiply π by the radius squared and by the height, then divide by 3. A cone with a 5 cm radius and 10 cm height holds 1/3 × π × 25 × 10 ≈ 261.8 cm³.
Measuring a pile or a slanted cone
Use the vertical height, not the slant length along the side. For a pile of material, measure around the base, divide by 2π to get the radius, and measure straight up from the ground to the peak.
The formula
V = 1/3 × π × r² × h
Examples
- Radius 5, height 10
Volume: 261.7993878
- Radius 3.5, height 12
Volume: 153.93804003
- Radius 20, height 45
Volume: 18,849.55592154
Cone volume examples
| Radius × height | Volume |
|---|---|
| 1 × 1 | 1.0472 |
| 2 × 3 | 12.5664 |
| 3 × 4 | 37.6991 |
| 5 × 10 | 261.7994 |
| 10 × 10 | 1,047.1976 |
| 10 × 30 | 3,141.5927 |
| 15 × 20 | 4,712.389 |
| 25 × 50 | 32,724.9235 |
Limitations and assumptions
Use the vertical height, not the slant length. The volume comes back in the cube of your unit.
Frequently asked questions
What is the volume of a cone with radius 3 and height 4?
About 37.7 cubic units: 1/3 × π × 9 × 4 = 12π.
How is a cone related to a cylinder?
A cone’s volume is exactly one third of the cylinder that fits around it.
Does the cone have to be upright?
No. A tilted (oblique) cone has the same volume as an upright one if the base and the vertical height are the same.