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) |
|---|---|
| 3 | 3.182 |
| 4.5 | 10.7392 |
| 6 | 25.4558 |
| 7.5 | 49.7184 |
| 9 | 85.9135 |
| 12 | 203.6468 |
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
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.
Frequently asked questions
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.