# Tetrahedron Volume Calculator

URL: https://speedycalculator.com/calculators/math/tetrahedron-volume/
Last updated: 2026-10-30

> The tetrahedron volume calculator finds the volume, height, surface area, surface-to-volume ratio and the insphere, midsphere and circumsphere radii of a regular tetrahedron from its edge.

## Inputs

- Edge a (cm, m, mm, in, ft, yd, km, mi)

## Results

- Volume
- Height
- Surface area
- Surface to volume ratio
- Insphere radius
- Midsphere radius
- Circumsphere radius

## Formula

```
V = a³/(6√2),  H = a√(2/3),  A = √3·a²
r_in = a/(2√6),  r_mid = a/(2√2),  r_circ = a√6/4
```

## Explanation

The regular tetrahedron – four equilateral triangles – is the simplest Platonic solid. Methane molecules, tetra-pak cartons, caltrops and four-sided dice have this shape.

### How to use the Tetrahedron Volume Calculator

- **Edge a**
- Every result field is editable: type into **Volume** or any other result and **Edge a** plus every other field update to match.

Results update as you type, and everything is calculated in your browser.

### How it works

Enter the edge length, or type any result to work back to the edge.

### What each result means

- **Volume** = [Edge a]^3÷(6×sqrt(2))
- **Height** = [Edge a]×sqrt(2÷3)
- **Surface area** = sqrt(3)×[Edge a]^2
- **Surface to volume ratio** = 6×sqrt(6)÷[Edge a]
- **Insphere radius** = [Edge a]÷(2×sqrt(6))
- **Midsphere radius** = [Edge a]÷(2×sqrt(2))
- **Circumsphere radius** = [Edge a]×sqrt(6)÷4

### Example values

How the main result changes when **Edge a** changes and everything else stays at the example values above:

Edge a (cm)Volume (cm³)33.1824.510.7392625.45587.549.7184985.913512203.6468

## Worked example

Inputs — Edge a: 6 cm.

Results — **Volume = 25.455844 cm³**; Height = 4.898979 cm; Surface area = 62.353829 cm²; Surface to volume ratio = 2.44949 cm⁻¹; Insphere radius = 1.224745 cm; Midsphere radius = 2.12132 cm; Circumsphere radius = 3.674235 cm.

## Key terms

- **Platonic solid**: A convex solid with identical regular faces.

## FAQ

**How many faces does a tetrahedron have?**
Four triangular faces, six edges, four vertices.

**What is the angle between faces?**
About 70.53°.

**Is every triangular pyramid a tetrahedron?**
Yes, but only one with equal edges is regular.

**What is the bond angle in methane?**
About 109.47°, the angle from the centre to two vertices.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [Wolfram MathWorld – Solid geometry](https://mathworld.wolfram.com/SolidGeometry.html)
- [Wolfram MathWorld – Regular tetrahedron](https://mathworld.wolfram.com/RegularTetrahedron.html)