What is the formula for the surface area of an icosahedron?

The surface area of a regular icosahedron is SA = 5√3 × a², where a is the length of one edge. Since the solid has 20 equilateral triangular faces and each triangle has area (√3/4)a², multiplying gives 20 × (√3/4)a² = 5√3 × a².

What units does this calculator support?

You can enter the edge length in millimeters (mm), centimeters (cm), meters (m), inches (in), or feet (ft). The surface area result is shown in the corresponding square unit.

Can I calculate the surface area for non-integer edge lengths?

Yes. The calculator accepts any positive decimal number as the edge length, such as 2.5 or 0.75.

What is the difference between surface area and volume of an icosahedron?

Surface area measures the total area of all 20 triangular faces (SA = 5√3 × a²), while volume measures the space enclosed inside (V = (5/12)(3 + √5)a³). This tool calculates surface area only.

Surface Area of an Icosahedron Calculator

Enter an edge length and instantly get the surface area of a regular icosahedron using SA = 5√3 × a².

Icosahedron Parameters

Edge Length (a)

Enter any positive number.

Formula

SA = 5√3 × a²

20 equilateral triangular faces, each with area (√3/4)a²

Result

Enter an edge length and click Calculate.

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Summary

A regular icosahedron is a Platonic solid with 20 equilateral triangular faces, 30 edges, and 12 vertices. Its surface area is calculated with the formula SA = 5√3 × a², where a is the edge length. This tool supports any unit of length and shows full step-by-step working.

How it works

Enter the edge length of the icosahedron in the input field.
Select your preferred unit of measurement (mm, cm, m, in, ft).
The calculator applies the formula SA = 5√3 × a².
Results are displayed instantly with step-by-step working.
Use the Copy button to copy the result to your clipboard.

Use cases

Geometry homework and exam preparation.
Calculating material needed to coat or paint an icosahedral object.
Architecture and 3D design projects involving Platonic solids.
Educational demonstrations of polyhedron surface area formulas.
DIY crafts such as paper or foam icosahedra.
Engineering and science models requiring precise surface measurements.

Frequently Asked Questions

Last updated: 2026-05-23 · Reviewed by Nham Vu