Tetrahedron Volume Calculator
A regular tetrahedron is one of the five Platonic solids, a three-dimensional shape with four identical equilateral triangular faces, four vertices, and six equal-length edges. It is the simplest of the Platonic solids. The volume of a regular tetrahedron is V = a³ / (6√2) or approximately 0.11785 * a³, where a is the length of any edge. The surface area is A = √3 * a², the sum of the areas of the four equilateral triangles. The height of the tetrahedron from its base to its apex is h = a * √(2/3). This calculator computes the volume, surface area, and height of a regular tetrahedron from the edge length.
Tetrahedron volume formulas
Volume = a³ / (6√2) ≈ 0.11785 * a³
Surface Area = √3 * a² ≈ 1.73205 * a²
Height = a * √(2/3) ≈ 0.81649 * a
Reference values
| Edge Length | Volume | Surface Area | Height |
|---|---|---|---|
| 1 cm | 0.12 cm³ | 1.73 cm² | 0.82 cm |
| 2 cm | 0.94 cm³ | 6.93 cm² | 1.63 cm |
| 5 cm | 14.73 cm³ | 43.30 cm² | 4.08 cm |
| 10 cm | 117.85 cm³ | 173.21 cm² | 8.16 cm |
Tetrahedron volume calculator: frequently asked questions
What is a tetrahedron?
A regular tetrahedron is a three-dimensional shape with four equilateral triangular faces, four vertices, and six edges of equal length. It is one of the five Platonic solids.
What is the volume formula?
For a regular tetrahedron with edge length a: V = a³ / (6√2) ≈ 0.11785 * a³. This formula derives from the geometry of the equilateral triangular faces.
What is the surface area formula?
The surface area is A = √3 * a², which is four times the area of one equilateral triangle face (√3/4 * a² each).
What is the height of a tetrahedron?
The height from the base to the apex is h = a * √(2/3) ≈ 0.81649 * a, where a is the edge length.
Where is a tetrahedron found in nature?
Tetrahedra appear in molecular geometry (methane and diamond crystal structures), in architecture, and in various mathematical and scientific contexts.
Official sources
- Khan Academy: Volume and surface area of solids.
- NIST: National Institute of Standards and Technology.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.