Regular Octahedron Calculator
Enter the edge length of a regular octahedron to find its volume, surface area, height, and inscribed and circumscribed sphere radii.
units
Volume of the regular octahedron
- 1
a² (scales surface)
2² = 4 - 2
a³ (scales volume)
2 × 4 = 8 - 3
Volume = (√2 ÷ 3) × a³
(√2 ÷ 3) × 8 = 3.7712One octahedron equals two square pyramids sharing a base, giving (√2/3)·a³.
How does this calculator work?
For a regular octahedron with edge a, the volume is (√2/3)·a³ and the surface area is 2√3·a². Its inscribed sphere has radius a√6/6, its circumscribed sphere has radius a√2/2, and the distance between opposite vertices is a√2. All values scale from the single edge length.
Formula
How this is calculated
A regular octahedron is a Platonic solid with 8 equilateral-triangle faces, 12 edges and 6 vertices. Every measurement depends only on the single edge length a, which must be a positive number expressed in your chosen unit.
The volume is V = (√2 / 3)·a³ and the total surface area is S = 2√3·a², the combined area of the eight equilateral faces. The radius of the inscribed sphere (touching each face) is r = a·√6/6, while the circumscribed sphere (passing through every vertex) has radius R = a·√2/2. The distance between two opposite vertices, the vertex-to-vertex height, is h = a·√2.
Volume scales with the cube of the edge and area with its square, so doubling a multiplies the volume by eight and the surface area by four. Length results share the edge unit, area is in squared units and volume in cubed units. The calculator rejects zero or negative edges since they do not describe a real solid.
Frequently asked questions
It has 8 congruent equilateral-triangle faces, 12 edges and 6 vertices, which is why it is also called an 8-faced solid.
The insphere radius r = a√6/6 is the radius of the largest sphere fitting inside and touching each face, while the circumsphere radius R = a√2/2 reaches every vertex.
Yes. The vertex-to-vertex height h = a√2 equals 2R, because opposite vertices lie on the circumscribed sphere.
Also known as
TG we-Calculate Editorial Team. (2026). Regular Octahedron Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/regular-octahedron-calculator
TG we-Calculate Editorial Team. "Regular Octahedron Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/regular-octahedron-calculator.
TG we-Calculate Editorial Team, "Regular Octahedron Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/regular-octahedron-calculator
@misc{wecalculate_regular_octahedron_calculator, title = {Regular Octahedron Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/regular-octahedron-calculator}}, year = {2026}, note = {TG we-Calculate} }
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