Calculators
Regular Octahedron Calculator
Calculate regular octahedron volume, surface area, face area, height, insphere radius, and circumsphere radius from edge length.
Measure a regular octahedron from its edge length.
A regular octahedron has eight equilateral triangle faces, twelve equal edges, and six vertices. For shared edge length a, volume = √2a³/3, total surface area = 2√3a², single face area = √3a²/4, opposite-vertex height = √2a, insphere radius = a/√6, and circumsphere radius = a/√2. The insphere touches every face; the circumsphere passes through every vertex. For a = 6, volume ≈ 101.823376491 cubic units, surface area ≈ 124.707658145 square units, and height ≈ 8.48528137424 units. These formulas apply only to regular octahedra. Use one consistent length unit; areas use square units and volume uses cubic units. Enter a positive edge length from 1e-50 to 1e50, including scientific notation. Results use browser floating-point arithmetic rounded to 12 significant digits. All calculations stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What is the volume of a regular octahedron?
Volume = √2a³/3, where a is the shared edge length. For edge length 6, volume is approximately 101.823376491 cubic units.
How do I calculate octahedron surface area?
Total surface area = 2√3a². Each of the eight equilateral triangle faces has area √3a²/4.
What does height mean here?
Height is the distance between opposite vertices: √2a. The circumsphere radius is half that distance, a/√2. The insphere radius is a/√6.
Can I use an irregular octahedron?
No. All twelve edges must have the same length and all eight faces must be equilateral triangles. Use any consistent length unit and enter an edge from 1e-50 to 1e50. Calculations run locally in your browser.