A pyramid is a polyhedron whose base is a polygon and whose other faces are triangles with a common apex. A pyramid is a special case of a cone.
A pyramid is regular if its base is a regular polygon and the apex projects onto the centre of the base.
Formula
The volume of a pyramid is V = 1/3 * S * H, where S is the base area and H the height (perpendicular from the apex to the base).
Example
A pyramid with a 6 × 6 m square base and 4 m height: S = 36 m², V = 36 × 4 / 3 = 48 m³ — exactly a third of a prism with the same base and height.
Units
The volume comes out in cubic units of the dimensions you enter: centimetres give cm³, metres give m³. Use the same unit for all dimensions. Conversion: 1 L = 1 dm³ = 1000 cm³, 1 m³ = 1000 L, 1 mL = 1 cm³.
Good to know
- The formula holds for any pyramid (triangular, square, hexagonal) as long as you know the base area.
- Square area is a², rectangle a × b, equilateral triangle a² × √3 / 4.
Where it is used
- Volume of a gravel or sand pile on a rectangular base, hip roofs and attics.
- Packaging, architecture, souvenirs, hoppers and funnels.
- Geometry problems and 3D modelling.
How to use
Enter the dimensions (decimals with a dot or comma) and press “Calculate”. You get the formula with your numbers and the result with a copy button, and the 3D model is redrawn to your dimensions.