Regular Octahedron Calculator
From one edge length, get the volume and the total surface area — the two numbers that describe any regular octahedron.
One input, two answers
Enter the edge length and the calculator returns the volume ((√2/3)·a³) and the surface area (2√3·a²) at once.
Keep units consistent
The edge length is unit-agnostic — your answers come back in the same unit (squared for the surface, cubed for the volume), so don't mix centimetres with inches.
What is a regular octahedron calculator?
One edge in, full solid out
A regular octahedron is one of the five Platonic solids: eight identical equilateral-triangle faces, like two square pyramids glued base to base. All twelve edges are the same length, so a single measurement — the edge length a — fixes the entire shape. This calculator turns that one number into the volume (how much it holds) and the total surface area (all eight faces). It is the tool for d8 gaming dice, fluorite and diamond crystals, molecular models, and any geometry homework where a regular octahedron shows up.
Enter the edge length in any length unit to get the volume and surface area instantly.
Two short formulas, both built from the single edge length a and a square root.
volume = (√2 / 3) × a³The surface area is the total of eight equilateral-triangle faces, which adds up to 2 × √3 × a². The volume, the space inside, is (√2 / 3) × a³: because an octahedron is two square pyramids joined at their base, it holds about four times as much as a regular tetrahedron of the same edge.
Suppose you have a regular octahedron with an edge length of 6.
Surface area
2 × √3 × 6² = 2 × √3 × 36 = 124.707658 square units — all eight faces.
Volume
(√2 / 3) × 6³ = (√2 / 3) × 216 = 101.823376 cubic units — the space inside.
The two outputs answer two different questions. The volume (about 101.823376 cubic units for a = 6) is how much the solid holds — useful for a crystal, a model, or a packing estimate. The single most useful insight is that an octahedron is two square pyramids joined at the base: its volume is (√2/3)·a³ ≈ 0.4714 × a³, roughly four times a regular tetrahedron of the same edge, yet still less than half of a cube of the same edge. The surface area (about 124.707658 square units) is the total of all eight faces — what you would paint or coat, and it scales with the square of the edge, so doubling the edge quadruples the surface while the volume grows eightfold. Because both quantities grow from the same single edge, scaling the model up or down is just a matter of rescaling a, and the octahedron's symmetry means it has no "top" or "front" to worry about.
The formulas are exact, but a couple of practical points are worth keeping in mind.
Regular octahedra and consistent units
These formulas describe a perfect regular octahedron — eight identical equilateral faces with every edge the same length. A non-regular octahedron (eight faces of different sizes, such as a stretched bipyramid) does not follow these formulas. The edge length is also unit-agnostic, so the answers are only meaningful if you keep one unit throughout: an edge in centimetres gives a volume in cubic centimetres and a surface area in square centimetres, never a mix.