A tetrahedron is a polyhedron with four triangular faces, three meeting at each vertex.
A tetrahedron is regular if all its faces are equilateral triangles, i.e. all edges are equal.
Formula
The volume of a regular tetrahedron is V = a3 * √2 / 12
Example
A regular tetrahedron with a 10 cm edge: V = 1000 × 1.414213 / 12 ≈ 117.85 cm³.
Units
The volume comes out in cubic units of the dimensions you enter: centimetres give cm³, metres give m³. Use the same unit for all dimensions. Conversion: 1 L = 1 dm³ = 1000 cm³, 1 m³ = 1000 L, 1 mL = 1 cm³.
Good to know
- A tetrahedron is a triangular pyramid, so for an irregular one use the pyramid formula:
V = S × H / 3. - It fills about 11.8% of a cube with the same edge.
Where it is used
- Tetra Pak packaging (the original milk carton shape), d4 dice.
- Tetrahedral molecules (methane, diamond), crystallography.
- Space frames and trusses, polygon meshes in 3D graphics and FEM.
How to use
Enter the dimensions (decimals with a dot or comma) and press “Calculate”. You get the formula with your numbers and the result with a copy button, and the 3D model is redrawn to your dimensions.