Pyramid Volume Calculator
A square pyramid is a three-dimensional shape with a square base and four triangular faces that meet at a point called the apex. The volume of a pyramid is exactly one-third the volume of a rectangular prism (or box) with the same base area and height, expressed as V = (1/3) * a² * h, where a is the side of the square base and h is the perpendicular height from the apex to the base. The slant height is the distance along a triangular face from the apex to the midpoint of a base edge, calculated as l = sqrt(h² + (a/2)²). This is different from the perpendicular height. The lateral surface area is the combined area of all four triangular faces: 2 * a * l. The total surface area includes the square base and all triangular faces: a² + 2 * a * l. This calculator computes the volume, slant height, and both lateral and total surface areas from the base side length and height.
Pyramid volume formulas
Volume = (1/3) * a² * h
Base Area = a²
Slant Height = √(h² + (a/2)²)
Lateral Surface Area = 2 * a * l
Total Surface Area = a² + 2 * a * l
Reference volumes
| Base Side | Height | Slant Height | Volume |
|---|---|---|---|
| 4 cm | 5 cm | 5.39 cm | 26.67 cm³ |
| 6 cm | 8 cm | 8.54 cm | 96.00 cm³ |
| 10 cm | 12 cm | 13.00 cm | 400.00 cm³ |
| 2 m | 3 m | 3.16 m | 4.00 m³ |
| 5 m | 6 m | 6.95 m | 50.00 m³ |
Pyramid volume calculator: frequently asked questions
What is the formula for pyramid volume?
The volume of a pyramid is V = (1/3) * base area * height. For a square pyramid, that becomes V = (1/3) * a² * h, where a is the side of the square base and h is the perpendicular height from the base to the apex.
What is slant height?
Slant height is the distance along a triangular face from the apex to the midpoint of a base edge. For a square pyramid, it is calculated as l = sqrt(h² + (a/2)²), where h is the height and a is the side length.
What is the lateral surface area of a pyramid?
The lateral surface area is the total area of all the triangular faces (not including the square base). For a square pyramid with four triangles, it equals 2 * a * l, where a is the base side and l is the slant height.
What is the total surface area?
The total surface area includes the square base and all four triangular faces. It is calculated as a² + 2 * a * l, which is the base area (a²) plus the lateral surface area (2 * a * l).
What are examples of pyramids?
Famous pyramids include the Egyptian pyramids of Giza, pyramid-shaped buildings, pyramid rooflines, Mayan pyramids, and pyramid-shaped sculptures or monuments.
Official sources
- Khan Academy: Volume and surface area of solids.
- NIST: National Institute of Standards and Technology.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.