Case 1
- Edge length (not the circumradius)
- 6
25.455844
Open with these valuesRegular Tetrahedron Volume Calculator
25.455844units³
Result: 25.455844 units³A regular tetrahedron is a triangular pyramid whose six edges are all equal, so one edge fixes it: V = a³ ÷ (6√2), a factor of about 0.117851. An edge of 6 holds 25.455844 cubic units. Its surface area √3 × a² and its height a × √(2÷3) stand in the table below.
Worked examples
Case 2
- Edge length (not the circumradius)
- 1
0.117851
Open with these valuesCase 3
- Edge length (not the circumradius)
- 10
117.851130
Open with these valuesHow it's calculated
V = a³ ÷ (6√2)
- StepMeasure one edge — not the radius of the sphere around the solid.
- StepCube it and divide by 6√2 ≈ 8.485281.
- ResultRead the volume in the cube of the unit you entered.
Reference table
| Edge a | Exact volume | Surface area | Height | Volume |
|---|---|---|---|---|
| 1 | 1 ÷ (6√2) | 1.732051 | 0.816497 | 0.117851 |
| 2 | 8 ÷ (6√2) | 6.928203 | 1.632993 | 0.942809 |
| 3.5 | 42.875 ÷ (6√2) | 21.217622 | 2.857738 | 5.052867 |
| 6 | 216 ÷ (6√2) | 62.353829 | 4.898979 | 25.455844 |
| 10 | 1000 ÷ (6√2) | 173.205081 | 8.164966 | 117.851130 |
Questions
How do I calculate the volume of a regular tetrahedron?
Cube the edge length and divide by 6√2. For an edge of 6 that is 216 ÷ 8.485281 ≈ 25.455844 cubic units, and multiplying the cube by √2 ÷ 12 ≈ 0.117851 gives the same answer.
What is a regular tetrahedron?
It is a triangular pyramid made of four identical equilateral triangles, with all six edges the same length. It is the simplest of the five Platonic solids, and a single edge length fixes the entire shape.
What is the surface area of a regular tetrahedron?
It is the total of four equilateral triangles, √3 × a², and the table above lists it for every example edge. For an edge of 6 that is about 62.353829 square units. Surface area scales with the square of the edge, so doubling the edge quadruples it.
How tall is a regular tetrahedron?
The height is the perpendicular distance from one face to the opposite vertex, a × √(2 ÷ 3) ≈ 0.816497 × a. For an edge of 6 that is about 4.898979, always a little under three quarters of the edge.
Do I enter the edge or the radius?
The edge, meaning the length of one of the six straight sides. The circumradius of a tetrahedron is only about 0.612 of its edge, so entering it here would give a badly wrong answer.
Which units does the answer use?
Whatever you entered, cubed. The height in the table stays in that same unit and the surface area is in its square.
Sources and last check
Information, not professional advice.