Volume of a Cone Formula
What is the formula for the volume of a cone?
Answer
Here r is the radius, h is the height, perpendicular to the base. The result comes out in cubic units.
Where the formula comes from
Fill a cone with water and pour it into a cylinder of the same base and the same height: it takes exactly three cones to fill it. So the cone is a third of πr²h. The one-third is not an approximation — it is exact for every cone, upright or leaning. (The slant-height relation below, and the surface-area formula, are a different matter: those hold only for a RIGHT circular cone, whose apex sits over the centre of the base.)
Worked examples
Let r = 3, h = 9. Then the volume of a cone ≈ 84.82 cubic units.
Let r = 2.5, h = 6. Then the volume of a cone ≈ 39.27 cubic units.
The common mistake
Using the slant height — the distance along the sloping side — instead of h. The height is the vertical drop from the tip to the centre of the base; the slant is always longer, and the two are linked by l² = r² + h².
Other quantities: Cone
Related Calculations
See Also
- Square Footage Calculator - Width × length in feet to square feet
- Square Feet to Square Meters (Sq Ft to Sq M) - Convert Square Feet to Square Meters
- Square Meters to Square Feet (Sq M to Sq Ft) - Convert Square Meters to Square Feet
- Gravel Calculator - Area to cubic yards, tons and coverage
- Topsoil Calculator - Cubic yards, weight and coverage for any area
- Multiplication Facts - Any two numbers from 1 to 9, with the working shown
<a href="https://calculat.io/en/geometry/shape-formula/volume--cone">Volume of a Cone Formula - Calculatio</a>
Values from the Formula (h = 9)
| If r = | Volume |
|---|---|
| 1 | ≈ 9.42 cubic units |
| 2 | ≈ 37.7 cubic units |
| 3 | ≈ 84.82 cubic units |
| 4 | ≈ 150.8 cubic units |
| 5 | ≈ 235.62 cubic units |
| 10 | ≈ 942.48 cubic units |