A pyramid holds exactly a third of the box built around it — not half, the same one-third relationship a cone has with its surrounding cylinder.
How it works
Squaring the base side length, multiplying by the height, and dividing by 3 gives the volume.
What this does not include
This does not include a rectangular-base pyramid (with two different base side lengths) or a pyramid with a triangular base — this calculator assumes a square base.
How to use this calculator
- Enter the base side length and the height.
A worked example
Square base side 6, height 9: volume = (6² × 9) ÷ 3 = 108.
What the variables mean
| Variable | Meaning |
|---|---|
| Base side | Length of one side of the square base |
| Height | Perpendicular distance from the base to the apex |
Edge cases worth knowing
A pyramid holds exactly a third of the box built around it — same base, same height — the identical one-third relationship a cone has to its surrounding cylinder.
A tilted (non-right) pyramid uses the same formula, as long as the perpendicular height — not a slanted edge — is what’s entered.
Frequently asked questions
Why a third, not a half?
It’s the same mathematical relationship a cone has to its surrounding cylinder — a direct result of how a pyramid’s cross-sectional area shrinks linearly from base to apex.
What’s a real-world example of this calculation?
Estimating the volume of an actual pyramid structure, a pyramidal roof section, or a pile of material shaped roughly like a pyramid.
What height should I use if the pyramid is tilted (not a “right” pyramid)?
The perpendicular height from the base to the apex — not the length of a slanted edge, which would overstate the true volume if used instead.
