What is the formula for the volume of a square pyramid?

V = (1/3) × a² × h, where a is the length of one side of the square base and h is the perpendicular height from the center of the base to the apex.

What is the difference between slant height and perpendicular height?

Perpendicular height (h) is the straight vertical distance from the base to the apex. Slant height is the distance along the triangular face from the midpoint of a base edge to the apex. This calculator uses perpendicular height.

Can I use different units for the base and height?

No — both dimensions must be in the same unit. Choose a unit from the dropdown and convert your measurements before entering them.

Why is the volume formula divided by 3?

A pyramid's volume is exactly one-third of the volume of a prism with the same base area and height. This is a fundamental result from integral calculus and Cavalieri's principle.

Does this work for rectangular pyramids?

No — this tool is specifically for square pyramids where all four base sides are equal. For a rectangular pyramid, the formula is V = (1/3) × l × w × h, where l and w are the length and width of the rectangular base.

Volume of a Square Pyramid Calculator

Name: Volume of a Square Pyramid Calculator
Availability: InStock
Author: Nham Vu

Enter the base side length and height to instantly calculate the volume of a square pyramid.

Pyramid Dimensions

All dimensions must use the same unit.

Unit

Base Side Length (a)

Perpendicular Height (h)

Formula

V = (1/3) × a² × h

a = base side length h = perpendicular height

Result

Enter dimensions to see the volume.

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