Octahedron Volume
Calculator
Results
- Volume
- 58.925565
- Total surface area
- 86.60254
Results
| Volume | 58.925565 |
| Total surface area | 86.60254 |
formula-map diagram
- Volume
- 58.925565
- Total surface area
- 86.60254
Formula map
Formula
V = (√2 ÷ 3) × a³= 58.925565098879
Note
Simplified model: these are the exact results of the stated idealised geometric formulas, assuming perfect shapes, exact inputs and consistent units. Real measurements carry error, and results such as the cyclic-quadrilateral area only hold when the figure truly satisfies the stated condition. Verify independently before relying on these figures.
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See all →Frequently asked questions
What is a regular octahedron, and what does the calculator need to find its volume?+
A regular octahedron is a solid with eight identical equilateral triangle faces, resembling two square pyramids joined base-to-base. Since all edges are equal length, the calculator only needs that single edge length to compute the volume.
What is the formula for the volume of a regular octahedron?+
Volume is V = (√2/3)a³, where a is the edge length. Like all regular polyhedra, volume scales with the cube of the edge length, so doubling the edge multiplies volume by eight.
How can I picture where the √2/3 factor in the formula comes from?+
A regular octahedron can be split into two identical square pyramids joined at their square bases; that square base has diagonal length a√2, giving side length a, and standard pyramid volume math for both halves combines into the √2/3 coefficient. Visualizing the two-pyramid decomposition makes the otherwise abstract formula more concrete.
Why does an octahedron hold more volume than a tetrahedron with the same edge length?+
With edge length a, an octahedron's volume (≈ 0.4714a³) is exactly four times a regular tetrahedron's volume (≈ 0.1178a³) for the same edge length. This is because the octahedron encloses more of the surrounding space per unit edge, having eight faces and more vertices than the tetrahedron's four faces.
Is the octahedron one of the five Platonic solids?+
Yes, the regular octahedron is one of the five Platonic solids (along with the tetrahedron, cube, dodecahedron, and icosahedron), each having identical regular polygon faces meeting at identical vertex angles. It is also the dual of the cube, meaning connecting the centers of a cube's faces produces an octahedron.