What is a regular octahedron?

A regular octahedron is one of the five Platonic solids. It has eight equilateral triangular faces, six vertices, and twelve edges all of equal length.

What is the formula for the surface area of a regular octahedron?

The surface area is SA = 2√3 × a², where a is the edge length. This simplifies to approximately SA ≈ 3.4641 × a².

Does this work for irregular octahedra?

No. This calculator is for regular octahedra only, where all eight faces are congruent equilateral triangles. Irregular octahedra require a different calculation.

What units can I use?

You can enter any positive number. The result is in the corresponding square unit — for example, entering centimeters gives square centimeters (cm²).

How is the formula derived?

A regular octahedron has 8 equilateral triangular faces. The area of one equilateral triangle with side a is (√3/4) × a². Multiplying by 8 gives 8 × (√3/4) × a² = 2√3 × a².

How precise is the calculation?

The calculation uses JavaScript full double-precision floating-point arithmetic (64-bit), which provides about 15 to 17 significant decimal digits of accuracy.

What is the formula for the octahedron?

For a regular octahedron with edge length a, the surface area is SA = 2√3 × a² and the volume is V = (√2/3) × a³. Both formulas come from the fact that the octahedron is built from eight equilateral triangles.

Surface Area of a Octahedron Calculator

Name: Surface Area of a Octahedron Calculator
Availability: InStock
Author: Nham Vu

Calculate the surface area of a regular octahedron from its edge length using SA = 2√3 × a².

Edge Length

Enter the length of one edge of the regular octahedron.

Edge Length (a)

Unit

Formula

SA = 2√3 × a²

≈ 3.46410162 × a²

Result

Enter an edge length and click Calculate.

Quick Examples

Summary

Calculate the surface area of a regular octahedron from its edge length using SA = 2√3 × a².

How it works

Enter the edge length of the regular octahedron.
Select the unit (mm, cm, m, in, ft) for your measurement.
The calculator applies the formula SA = 2√3 × a².
Surface area is displayed in both standard and scientific notation.
Use the Copy button to copy the result to your clipboard.

Use cases

Calculate paint or material coverage for octahedral models.
Solve geometry homework involving Platonic solids.
Estimate surface area for crystal structures in chemistry.
Verify results for 3D printing and engineering projects.
Compare surface areas of different octahedron sizes.
Convert between unit systems with the built-in unit selector.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu