Calculators
Regular Icosahedron Calculator
Calculate regular icosahedron volume, total surface area, and triangular face area from edge length, privately in your browser.
Measure a regular icosahedron from its edge length.
A regular icosahedron has twenty equilateral triangle faces, thirty equal edges, and twelve vertices. For shared edge length a, volume V = 5(3 + √5)a³/12, single face area F = √3a²/4, and total surface area A = 20F = 5√3a². For a = 2, volume is approximately 17.453559925 cubic units, face area is 1.73205080757 square units, and total surface area is 34.6410161514 square units. These formulas require a regular icosahedron; they do not describe arbitrary twenty-faced solids. 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 formula?
For edge length a, volume = 5(3 + √5)a³/12. An edge length of 2 gives approximately 17.453559925 cubic units.
How is surface area calculated?
Each equilateral triangle face has area √3a²/4. Multiply by twenty to obtain total surface area: 5√3a².
Can I use any twenty-faced solid?
No. This calculator requires a regular icosahedron with twenty congruent equilateral triangle faces and thirty equal edges.
Which units and inputs are supported?
Use any consistent length unit and a positive edge from 1e-50 to 1e50. Scientific notation is accepted. Areas use squared units and volume uses cubed units; results are rounded to 12 significant digits. Inputs stay in your browser.