# Triangular Pyramid Volume Calculator

Calculate the volume of a triangular pyramid or tetrahedron from base area and height. Supports regular tetrahedrons and custom base triangles. Free online calculator.

## What this calculates

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.

## Inputs

- **Input Method** — options: Base Area + Height, Base Triangle Dimensions + Height, Regular Tetrahedron (Edge Length) — Choose how you want to provide the dimensions.
- **Base Area** — min 0 — The area of the triangular base.
- **Base Triangle Length** — min 0 — The length of the base of the triangular face.
- **Base Triangle Height** — min 0 — The height of the triangular base (perpendicular to base length).
- **Pyramid Height** — min 0 — The perpendicular height from the base to the apex.
- **Edge Length** — min 0 — Edge length for a regular tetrahedron (all edges equal).

## Outputs

- **Volume** — The volume of the triangular pyramid.
- **Base Area** — The area of the triangular base used in the calculation.
- **Pyramid Height** — The perpendicular height from base to apex.

## Details

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.

## Frequently Asked Questions

**Q: What is the formula for the volume of a triangular pyramid?**

A: The volume of a triangular pyramid is V = (1/3) x base area x height. If the base is a triangle with base b and height h_b, then base area = (1/2) x b x h_b. For a regular tetrahedron with edge length a, the volume simplifies to V = a^3 / (6 x sqrt(2)).

**Q: What is the difference between a triangular pyramid and a tetrahedron?**

A: A triangular pyramid and a tetrahedron are the same shape. Both have four triangular faces. The term 'regular tetrahedron' specifically refers to one where all four faces are equilateral triangles and all six edges are the same length.

**Q: How do I find the height of a regular tetrahedron?**

A: For a regular tetrahedron with edge length a, the height is h = a x sqrt(2/3), which equals approximately 0.8165 x a. This is the perpendicular distance from any face to the opposite vertex.

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Source: https://vastcalc.com/calculators/math/triangular-pyramid-volume
Category: Math
Last updated: 2026-04-08