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Pyramid with polygonal base properties
Cone properties
Cube properties
Cylinder properties
Tetrahedron properties
All solids
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Properties of Pyramid

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

a =
h =
Geometric properties:
Volume =
Surface area =
Base area =
Lateral surface area =
Lateral edge length L =
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Definitions

Geometry

The pyramid is a solid object with a polygonal base and side faces that converge to a single point, the apex. Typically the most recognizable pyramid is the one with square base. This type is examined in this page. A square based pyramid, has 5 faces, 8 edges and 5 vertices.

The volume of a square based pyramid is given by the formula:

\[ V = \frac{1}{3} a^2 h \]

where a the length of a base side and h the height of the pyramid. This formula is derived from the following general expression, that covers all pyramids, with any polygonal base, and also the cone:

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

where \(A_b\) the base area.

The surface area of one side face of the square based pyramid, can be found using the following formula:

\[ A_{f0} = \frac{a}{2}\sqrt{h^2 + \frac{a^2}{4}} \]

Since there are four side faces and the area of the square base is equal to \(a^2\), the total surface area of the square based pyramid is:

\[ A = a^2 + 4A_{f0} \]

The edge, that connects a base vertex with apex, has a length equal to:

\[ L = \sqrt{h^2 + \frac{a^2}{2}} \]

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