What is a regular dodecahedron?

A regular dodecahedron is one of the five Platonic solids. It has 12 congruent regular pentagonal faces, 30 edges, and 20 vertices. All edges are equal in length.

What is the formula for the surface area of a dodecahedron?

The surface area is SA = 3 * sqrt(25 + 10*sqrt(5)) * a^2, where a is the edge length. This simplifies to approximately 20.6457 * a^2.

What units does this calculator use?

You enter the edge length in your chosen unit (millimeters, centimeters, meters, inches, or feet). The surface area result is expressed in the same unit squared (e.g., cm^2).

How many faces does a dodecahedron have?

A regular dodecahedron has exactly 12 pentagonal faces. The total surface area is the sum of the areas of all 12 pentagons.

Can I use this for irregular dodecahedra?

No. This formula applies only to a regular dodecahedron where all 12 faces are congruent regular pentagons and all edges are equal.

Surface Area of a Dodecahedron Calculator

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

Enter the edge length of a regular dodecahedron and instantly get its total surface area.

Dodecahedron Edge Length

Enter the length of one edge of the regular dodecahedron.

Edge Length (a)

Formula

SA = 3 × √(25 + 10√5) × a²

The constant 3√(25+10√5) ≈ 20.6457

Enter an edge length to see the result

Summary

Enter the edge length of a regular dodecahedron and instantly get its total surface area.

How it works

Enter the edge length of the dodecahedron in the input field.
Choose your preferred unit (mm, cm, m, in, ft).
The calculator applies the formula SA = 3 * sqrt(25 + 10*sqrt(5)) * a^2.
The total surface area is displayed instantly in the same unit squared.
Copy the result or try another edge length.

Use cases

Computing surface area for 3D printing or CNC machining a dodecahedron.
Solving geometry homework or exam problems involving Platonic solids.
Estimating paint or coating material needed for a dodecahedral object.
Verifying hand calculations in architectural or design projects.
Teaching or learning solid geometry and polyhedron properties.
Game design or tabletop RPG dice (d12) dimension calculations.

Frequently Asked Questions

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