How cone volume is calculated
A cone holds one third of the cylinder that fits around it, so the base area times the height is divided by three.
V = (1/3) × π × r² × h
- π (pi) is about 3.14159, r is the radius of the base and h is the vertical height.
- Square the radius, multiply by π for the base area, multiply by the height, then divide by 3.
- Diameter is radius × 2. If you measured across the base, enter the diameter and this calculator halves it for you.
- The result is in cubic units of whatever you measured in: cubic centimetres divide by 1,000 for litres; a cubic metre is already 1,000 litres.
Worked example — A cone with a 10 cm radius and 30 cm height holds π × 10² × 30 ÷ 3 = 3,141.59 cm³, about 3.14 litres — exactly one third of the 9.42 litres the matching cylinder holds.
Common heaps and containers
| Diameter | Height | Measured in | Volume | Litres | US gallons |
|---|---|---|---|---|---|
| 1 | 0.7 | Metres | 0.18 m³ | 183.26 L | 48.41 gal |
| 2 | 1.2 | Metres | 1.26 m³ | 1,256.64 L | 331.97 gal |
| 3 | 1.5 | Metres | 3.53 m³ | 3,534.29 L | 933.66 gal |
| 8 | 12 | Centimetres | 201.06 cm³ | 0.2 L | 0.05 gal |
| 15 | 20 | Centimetres | 1,178.1 cm³ | 1.18 L | 0.31 gal |
Swipe the table sideways to see the rest.
A heap is measured straight across the base, then from the ground to the top. Anything not listed here goes in the calculator above.
Things to consider
- A heap of sand, gravel or mulch is roughly a cone: measure straight across the base, then from the ground to the top.
- Use the inside height of a cup, funnel or hopper, not the outside.
- In a cone standing on its tip, the liquid forms a smaller cone — measure the liquid's depth and the width of its surface.
- A leaning cone holds the same volume as an upright one if the base and vertical height match.
Frequently asked questions
What is the formula for the volume of a cone?
V = (1/3) × π × r² × h — one third of pi times the radius squared times the height.
Why is a cone one third of a cylinder?
Fill a cone and pour it into the cylinder with the same base and height: it takes exactly three cone-fulls.
How do I find the volume from the diameter?
Divide the diameter by 2 to get the radius, or enter it in the diameter field and this calculator halves it for you.
How do I measure a pile of gravel or sand?
Measure across the widest part of the base for the diameter, then from the ground to the top for the height.
How many litres is a cubic metre?
1,000 litres. A cubic metre is also 1,000,000 cubic centimetres.
Results are estimates for general information only, not financial, medical or professional advice.