Cone Volume Calculator: (1/3)πr²h Formula Online

Cone Volume Calculator

Find the volume of a right circular cone when you know the base radius and perpendicular height. The result is in cubic units matching the length unit you use (millimetres give mm³, inches give in³, and so on).

Radius (r)

Half of the base diameter, in any length unit.

Height (h)

Perpendicular distance from the base to the tip, same unit as r.

Enter a positive radius.

How it works

Find the volume of a right circular cone when you know the base radius and perpendicular height. The result is in cubic units matching the length unit you use (millimetres give mm³, inches give in³, and so on).

The Formula

Let r be the radius of the circular base and h the perpendicular height from the base to the apex.

V = (1/3) π r² h

A cone with the same base and height as a cylinder has exactly one-third of that cylinder’s volume.

Worked Example

Paper cup style cone
If r = 4 cm and h = 9 cm, then r² = 16 and V = (1/3)π × 16 × 9 = 48π ≈ 150.8 cm³. A cylinder with the same r and h would hold about 452.4 cm³, three times as much.

Tips, Assumptions & Limitations

Use the perpendicular height (top to base), not slant height, in this formula.
Keep radius and height in the same length unit before reading the volume.
If you know diameter d, set r = d ÷ 2.

FAQ

Use V = (1/3)πr²h with the radius r and the perpendicular height h. Slant height is only needed for surface-area questions, not this volume formula.

For a fixed base area and height, the cone’s interior tapers linearly from base to apex, which geometrically accounts for the factor of one-third compared with a full prism or cylinder of the same base and height.

Yes. Enter r and h in the same unit; the volume appears in the matching cubic unit (ft³, m³, etc.). This is an educational model of a right circular cone, not a construction or engineering certification.