Triangular Pyramid Volume Calculator

This triangular pyramid volume calculator works out the volume of a pyramid that stands on a triangular base. Enter the base triangle base and its height to fix the base area, add the vertical height of the pyramid, choose your unit, and it returns the volume. As with every pyramid, the volume is one third of the base area times the perpendicular height. The base area of the triangle is one half times its base times its height. The calculator is unit agnostic, so metres give cubic metres and centimetres give cubic centimetres. Use it for geometry study, model making, roof and tent shapes, or any three sided pyramid. If your base triangle is given as an area already, you can reverse engineer a base and height that multiply to twice that area, or use the general rule that the volume is a third of the base area times the height. The vertical height is the straight up distance to the apex, not the slanted face. The formula, a worked example and the assumptions are set out below.

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Base triangle base

Base triangle height

Pyramid height

Units

Base area

Pyramid height

The formula

The volume of a pyramid is one third of the base area times the height. The triangular base area is one half base times height, so V = (1/3) times (1/2 b h_b) times H, where b and h_b describe the base triangle and H is the pyramid height.

Worked example

A triangular pyramid whose base triangle is 6 wide and 4 tall has a base area of 12. With a pyramid height of 9 the volume is (1/3) times 12 times 9 = 36. Enter those values above to confirm.

Frequently asked questions

What is the triangular pyramid volume formula?

V = one third times the base triangle area times the pyramid height, and the base triangle area is one half its base times its height.

Is this the same as a tetrahedron?

A tetrahedron is a triangular pyramid. This calculator takes the base triangle and the vertical height directly, which works for any triangular pyramid, regular or not.

Which height do I use?

Two heights are involved: the height of the base triangle, and the vertical height of the pyramid from base to apex. Enter both where asked.

Who this calculator is for

This calculator is for students, model makers and designers who need the volume of a triangular based pyramid.

What this calculator assumes

The base is a triangle of the base and height you enter.
The pyramid height is the perpendicular height to the apex.
The volume is in the cube of your chosen unit.
Results are rounded for display.

Formula and sources

Related calculators

Rectangular Pyramid Volume Calculator: pyramid with a rectangular base.
Triangle Calculator: triangle area and sides.
Volume Calculator: volume of common solids.
Cylinder Volume Calculator: volume of a cylinder.

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