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Pyramid properties
Pyramid with polygonal base properties
Cube properties
Cylinder properties
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Properties of Cone

- By Dr. Minas E. Lemonis, PhD - Updated: March 3, 2019

This tool calculates the basic geometric properties of a cone, with a circular base. Enter the shape dimensions 'r' and 'h' below. The calculated results will have the same units as your input. Please use consistent units for any input.

r =
h =
icon

Geometric properties:
Volume =
Surface area =
Base area =
Lateral surface area =
Lateral height L =
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Definitions

Geometry

The cone is a solid object with a circular base and a side surface that converges to a single point, the apex.

The volume of a cone is given by the formula:

V = \frac{1}{3} \pi r^2 h

where r the radius of the circular base and h the height of the cone. This formula is derived from the following general expression, that also covers all pyramids, with any polygonal base:

V = \frac{1}{3} A_b h

where A_bthe base area.

The lateral surface area of the cone can be found using the following formula:

A_f = \pi r L

where L the lateral height of the cone, which is easily found as:

L = \sqrt{h^2+r^2}

Since the area of the circular base is equal to \pi r^2, the total surface area of the cone is:

A = \pi r^2 + \pi r L

See also
Pyramid properties
Pyramid with polygonal base properties
Cube properties
Cylinder properties
Tetrahedron properties
All solids
All Geometric Shapes tools