Tetrahedron Calculator

Tetrahedron: how to find the surface area and volume when one side length is given, and how to find the surface area and side length when the volume is given.

Tetrahedron Calculation Method

Calculate the volume and surface area of a cube from its side length.

Formula for the volume

Formula for the area

Formula for the height of a regular tetrahedron

The side length (a) of the tetrahedron is 0 .

The volume (V) of the tetrahedron is 0 .

The area (S) of the tetrahedron is 0 .

The height (h) of the tetrahedron is 0 .

About This Calculator

A regular tetrahedron is the simplest Platonic solid: four equilateral-triangle faces meeting at four vertices. Its volume and surface area both follow directly from the edge length.

Enter the side length to get the surface area and volume of a regular tetrahedron.

A regular tetrahedron of edge a has volume a³/(6√2) ≈ 0.1179a³ and surface area √3a². For a = 6 the volume is 25.46 and the surface area 62.35. It is the simplest Platonic solid, the only one that is its own dual, and four spheres pack around a point in its arrangement.

Key Formula:V = a³ / (6√2) · Surface area = √3 × a²

Frequently Asked Questions

How many faces, edges and vertices does a tetrahedron have?

A tetrahedron has 4 faces, 6 edges and 4 vertices, satisfying Euler's formula F + V − E = 2. It is the only Platonic solid without a pair of opposite parallel faces.

Where are tetrahedra used in practice?

Their rigid shape makes them popular in structural trusses, and the tetrahedral geometry underlies the bond angles in methane and other molecules with four substituents.

Why is the volume factor 1/(6√2)?

The base is an equilateral triangle of area (√3/4)a² and the height is a√(2/3). One third of base times height simplifies to a³/(6√2), about 0.1179a³.

How do I find the height of a regular tetrahedron?

It is a√(2/3) ≈ 0.8165a, so an edge of 6 gives 4.899. The centre of mass lies a quarter of the height above the base.

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Sources & last update

2026-10-19