A pyramid with a triangular base (a tetrahedron shape), distinct from the more common rectangular-base pyramid.
How it works
The triangular base’s area is found first (base times height, divided by 2), then multiplied by the pyramid’s height and divided by 3.
What this does not include
This does not include rectangular-base pyramids — for those, use this site’s general volume calculator instead, which covers that shape.
How to use this calculator
- Enter the triangular base’s dimensions and the pyramid’s height.
A worked example
A triangular pyramid (tetrahedron-style) with triangle base 6, triangle height 4, and pyramid height 9: volume = (⅓) × (½ × 6 × 4) × 9 = 36.
What the variables mean
| Variable | Meaning |
|---|---|
| Base, triangle height | Dimensions of the triangular base |
| Pyramid height | Perpendicular height from the base to the apex |
Edge cases worth knowing
Every pyramid’s volume formula includes a factor of ⅓, regardless of the base shape — a pyramid always holds exactly one-third the volume of a prism sharing the same base and height.
A base of zero collapses the triangular base entirely, leaving no pyramid to measure, so the calculator declines to show a result.
Frequently asked questions
Why does every pyramid’s volume divide by 3, regardless of base shape?
It’s a general geometric relationship — any pyramid holds exactly a third of the volume of a prism with the same base and height, whether that base is a triangle, rectangle, or any other polygon.
Is a triangular pyramid the same as a tetrahedron?
Yes, when all four faces are triangles — a tetrahedron is specifically a triangular pyramid with a triangular base and three triangular sides.
Does the triangle base need to be equilateral?
No — this formula works for any triangle base, using its own base and perpendicular height, regardless of the triangle’s specific shape.
