Pyramid Volume Calculator
From a base edge and a height, get the volume, the base area, and the slant height — the three numbers that describe a right square pyramid.
Two inputs, three answers
Enter the base edge and the height and the calculator returns the volume ((1/3)a²h), the base area (a²), and the slant height (√(h²+(a/2)²)) at once.
Keep units consistent
The base edge and height are unit-agnostic — your answers come back in the same unit (squared for the base area, cubed for the volume), so don't mix centimetres with inches.
What is a pyramid volume calculator?
Base edge and height in, full pyramid out
A pyramid volume calculator turns two measurements — the base edge and the vertical height — into the numbers that describe a whole right square pyramid: how much it holds (volume), the area of its square footprint (base area), and the length of the slope up the middle of a triangular face (slant height). This tool assumes a square base with the apex straight over its centre, so those two inputs are all you need. That covers monuments and roofs, pyramid-shaped moulds and tents, packaging, piles tapering to a point, and any geometry homework where a square pyramid shows up.
Enter the base edge and height in any length unit to get the volume, base area, and slant height instantly.
Three short formulas, all built from the base edge a and the height h.
volume = (1/3) × a² × hThe base area is just the square base, a². The volume — the space inside — is one-third of the base area times the height: (1/3) × a² × h. A pyramid holds exactly one-third of the prism with the same base and height. The slant height runs from the midpoint of a base edge up the middle of a triangular face to the apex; by the Pythagorean theorem it is √(h² + (a/2)²), using half the base edge as the horizontal leg.
Suppose you have a square pyramid with a base edge of 6 and a height of 10.
Base area
6² = 36 square units — the square footprint of the pyramid.
Volume
(1/3) × 36 × 10 = 120 cubic units — exactly one-third of the matching box.
Slant height
√(10² + 3²) = √109 ≈ 10.440307 — the slope up a triangular face.
The three outputs answer three different everyday questions. The volume (exactly 120 cubic units for a = 6, h = 10) is how much the pyramid holds — the sand in a pyramid-shaped pile, the space inside a tent, the material in a moulded block. The single most useful insight is that a pyramid is exactly one-third of the prism with the same base and height: three full pyramids fill the matching square box, which is why a tapering shape contains far less than it looks. The base area (36 square units here) is the square footprint, the patch of ground the pyramid covers and the starting point of the volume formula. The slant height (about 10.440307) is the slope you would measure up the middle of a triangular face; because it is the hypotenuse of the height and half-edge triangle, it is always longer than the vertical height — never confuse the two when cutting a face or sizing a tarp. Keep one length unit throughout and the three numbers stay consistent: same units for the slant height, squared for the base area, cubed for the volume.
The formulas are exact, but a couple of practical points are worth keeping in mind.
Right square pyramids and consistent units
These formulas describe a perfect right square pyramid — a square base with the apex straight above its centre. An oblique pyramid (tip off to one side), a pyramid with a rectangular or triangular base, or a frustum (with the tip cut off) will differ from the computed value. The base edge and height are also unit-agnostic, so the answers are only meaningful if you keep one unit throughout: a base edge and height in centimetres give a volume in cubic centimetres and a base area in square centimetres, never a mix.