How to Calculate Tetrahedron
What is Tetrahedron?
A regular tetrahedron is one of the five Platonic solids, consisting of four equilateral triangular faces. It is the simplest and most symmetric 3D shape with flat faces.
Formula
V = a³/(6√2); SA = √3 a²; h = a√(2/3)
- a
- edge length (length)
- V
- volume (length³)
- SA
- surface area (length²)
- h
- height (length)
Step-by-Step Guide
- 1Volume = a³/(6√2)
- 2Surface area = √3 × a²
- 3Height h = a√(2/3)
- 4Edge length a determines all dimensions
Worked Examples
Input
Edge a = 6
Result
Volume ≈ 25.46, SA ≈ 62.35
Input
Edge a = 4
Result
Volume ≈ 7.54, SA ≈ 27.71
Frequently Asked Questions
What is the simplest 3D shape?
The tetrahedron (4 triangular faces) is the simplest 3D polyhedron, just as the triangle is the simplest 2D polygon.
How many vertices, edges, and faces does a tetrahedron have?
4 vertices, 6 edges, and 4 equilateral triangular faces.
Is a tetrahedron the same as a triangular pyramid?
Yes, a regular tetrahedron is a specific type of triangular pyramid where all four faces are equilateral triangles.
Ready to calculate? Try the free Tetrahedron Calculator
Try it yourself →