Case 1
- Edge length (not the circumradius)
- 6
101.823376
Open with these valuesRegular Octahedron Volume Calculator
101.823376units³
Result: 101.823376 units³A regular octahedron is two square pyramids joined base to base, and all twelve edges are equal: V = √2 ÷ 3 × a³, a factor of about 0.471405. An edge of 6 holds 101.823376 cubic units. The surface area 2√3 × a² stands in the table below.
Worked examples
Case 2
- Edge length (not the circumradius)
- 1
0.471405
Open with these valuesCase 3
- Edge length (not the circumradius)
- 10
471.404521
Open with these valuesHow it's calculated
V = √2 ÷ 3 × a³
- StepMeasure one edge — not the radius of the sphere around the solid.
- StepCube it and multiply by √2 ÷ 3 ≈ 0.471405.
- ResultRead the volume in the cube of the unit you entered.
Reference table
| Edge a | Exact volume | Surface area | Volume |
|---|---|---|---|
| 1 | √2 ÷ 3 | 3.464102 | 0.471405 |
| 2 | √2 × 8 ÷ 3 | 13.856406 | 3.771236 |
| 3.5 | √2 × 42.875 ÷ 3 | 42.435245 | 20.211469 |
| 6 | √2 × 216 ÷ 3 | 124.707658 | 101.823376 |
| 10 | √2 × 1000 ÷ 3 | 346.410162 | 471.404521 |
Questions
How do I calculate the volume of a regular octahedron?
Cube the edge length and multiply by √2 ÷ 3, a factor of about 0.471405. For an edge of 6 that is 0.471405 × 216 ≈ 101.823376 cubic units.
What is a regular octahedron?
It is one of the five Platonic solids: eight identical equilateral triangles, shaped like two square pyramids joined base to base. All twelve edges are the same length, so a single edge measurement fixes the whole shape. A d8 gaming die is a regular octahedron.
What is the surface area of a regular octahedron?
It is the total of eight equilateral triangles, 2 × √3 × a², and the table above lists it for every example edge. For an edge of 6 that is about 124.707658 square units. Surface area scales with the square of the edge, so doubling the edge quadruples it.
Do I enter the edge or the radius?
The edge, meaning the length of one of the twelve straight sides. The circumradius of an octahedron is exactly half the edge times √2, so convert it before entering.
How does an octahedron compare to a tetrahedron?
At the same edge length the octahedron holds exactly four times as much. Its factor is √2 ÷ 3 ≈ 0.4714 against √2 ÷ 12 ≈ 0.1179 for the tetrahedron.
Which units does the answer use?
Whatever you entered, cubed. An edge in centimetres gives cubic centimetres, an edge in inches cubic inches. The surface area in the table follows the same unit squared.
Sources and last check
Information, not professional advice.