Pyramid Volume
Calculate the volume of any pyramid from base area and height for square, rectangular, triangular, and polygonal pyramids. Free pyramid volume calculator with formula.
About This Calculator
The pyramid volume calculator computes the volume of any pyramid given its base area and height. The universal formula V = (1/3) x B x h works for all pyramid types: square pyramids, rectangular pyramids, triangular pyramids (tetrahedrons), pentagonal pyramids, hexagonal pyramids, and any polygonal base pyramid -- both right and oblique.
Formula
V = (1/3) x B x h where B is the area of the base and h is the perpendicular height from base to apex. This is the same general formula used for cones and is derived from the fact that a pyramid occupies exactly one-third the volume of a prism with the same base and height.
How to Use
Enter the base area in square units and the height in the same linear units. Click Calculate to get the volume. Use the shareable permalink to save or share your calculation.
Examples
Square pyramid: Base side = 6 units, height = 8 units. Base area = 36 sq units. Volume = (1/3) x 36 x 8 = 96 cubic units.
Rectangular pyramid: Base length = 10, width = 4, height = 9. Base area = 40 sq units. Volume = (1/3) x 40 x 9 = 120 cubic units.
Triangular pyramid: Base area = 15 sq units, height = 12 units. Volume = (1/3) x 15 x 12 = 60 cubic units.
Regional Notes
The formula is universal. In the US measurements are often in feet and inches (cubic ft); in the UK and India meters and centimeters (cubic m) are common. The calculator accepts any consistent unit system.
Frequently Asked Questions
What is the formula for pyramid volume?
The volume of any pyramid is V = (1/3) x base area x height. This formula works for all pyramid types including square, rectangular, triangular, and hexagonal pyramids, for both right and oblique pyramids.
How do I find the base area of a pyramid?
For a square base, area = side squared. For a rectangular base, area = length x width. For a triangular base, area = (1/2) x base x triangle height. For a regular polygon with n sides, area = (n/4) x side squared x cot(pi/n).
What is the difference between a right pyramid and an oblique pyramid?
In a right pyramid the apex is directly above the base centroid, making all lateral edges equal. In an oblique pyramid the apex is offset. The volume formula V = (1/3) x base area x height works for both types.
How do I calculate the volume of a square pyramid?
For a square pyramid with base side a and height h: V = (1/3) x a squared x h. For example, a pyramid with base side 5 units and height 10 units has volume = (1/3) x 25 x 10 = 83.33 cubic units.
How do I calculate the volume of a triangular pyramid (tetrahedron)?
For a triangular pyramid with base area A and height h: V = (1/3) x A x h. For a regular tetrahedron with edge length a: V = a cubed / (6 x sqrt(2)).
What units should I use for pyramid volume?
Pyramid volume is in cubic units. Use base area in square units and height in the same linear units. For meters: m squared x m = cubic meters. For feet: sq ft x ft = cubic feet.
Is the pyramid volume formula same for all countries?
Yes, the formula V = (1/3) x base area x height is universal and used worldwide. Only the unit systems differ: metric (meters, centimeters) in India, UK, and Europe; imperial (feet, inches) in the US.