Volume of a Pyramid Calculator
Find the volume of any pyramid by selecting the base shape and entering the dimensions. This calculator supports square, rectangular, and triangular bases, and also computes the base area and slant height.
A pyramid is a 3D solid with a polygonal base and triangular faces that meet at a single apex. The volume formula for any pyramid is V = (1/3) x base area x height, where height is the perpendicular distance from the base to the apex.
For a square-based pyramid with side s and height h, the volume is V = (1/3) x s² x h. For a rectangular base with length l and width w, V = (1/3) x l x w x h. For a triangular base with base b and base height h_b, the base area is (1/2) x b x h_b, giving V = (1/6) x b x h_b x h.
The factor of 1/3 in the pyramid volume formula comes from the fact that a pyramid is exactly one-third of a prism with the same base and height. This can be proven by dividing a cube into three congruent pyramids. The slant height is the distance from the apex to the midpoint of a base edge, useful for calculating the lateral surface area.