Triangular Pyramid Volume Calculator
Find the volume of any triangular pyramid (tetrahedron) using the base area and height, the base triangle dimensions, or simply the edge length for a regular tetrahedron. Enter your values and get the result instantly.
A triangular pyramid is a solid with four triangular faces. When all four faces are equilateral triangles, it is called a regular tetrahedron. The volume formula is the same as for any pyramid: V = (1/3) x base area x height.
Three Ways to Calculate:
- Base area + height: If you already know the base area, just multiply by the height and divide by 3.
- Base triangle dimensions: If you know the base and height of the triangular base, the calculator finds the base area first (1/2 x base x triangle height), then uses the pyramid formula.
- Regular tetrahedron: For a tetrahedron where all edges have the same length a, the volume is a^3 / (6 x sqrt(2)). The height of a regular tetrahedron is a x sqrt(2/3).
Why the 1/3 factor?
The 1/3 in the pyramid volume formula comes from calculus. If you slice a pyramid into infinitely thin horizontal layers, each layer is a triangle whose area shrinks quadratically as you move toward the apex. Integrating these areas gives exactly one-third of the prism volume with the same base and height.