What is a regular dodecahedron?

A regular dodecahedron is a Platonic solid with 12 congruent regular pentagonal faces, 30 edges, and 20 vertices. Every edge has the same length and every face is an identical regular pentagon.

What is the formula for the volume of a dodecahedron?

The exact formula is V = (15 + 7√5) / 4 × a³, where a is the edge length. The numerical coefficient (15 + 7√5) / 4 ≈ 7.6631 is derived from the geometry of the regular pentagon.

What units does this calculator support?

You can enter the edge length in millimeters, centimeters, meters, inches, or feet. The volume result is automatically expressed in the corresponding cubic unit (mm³, cm³, m³, in³, or ft³).

How accurate is the result?

The calculator uses full IEEE 754 double-precision arithmetic and displays up to 6 significant figures. For most practical purposes this is more than sufficient.

Can I use this for a D12 gaming die?

Yes. Standard D12 dice have an edge length of roughly 14–16 mm depending on the manufacturer. Enter that length in mm to get the volume in mm³, then convert to cm³ by dividing by 1000.

Volume of a Dodecahedron Calculator

Enter the edge length of a regular dodecahedron and instantly get its volume using the exact formula V = (15+7√5)/4 × a³.

Dodecahedron Edge Length

Enter the length of one edge. All 30 edges of a regular dodecahedron are equal.

Edge Length (a)

Formula

V = (15 + 7√5) / 4 × a³

Coefficient ≈ 7.66312

Result

Enter an edge length and click Calculate.

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Summary

A regular dodecahedron is one of the five Platonic solids, composed of 12 regular pentagonal faces, 30 edges, and 20 vertices. This calculator computes its volume from a single edge length using the formula V = (15 + 7√5) / 4 × a³. All you need is one measurement to get an exact result instantly.

How it works

Enter the edge length of the regular dodecahedron.
Select your preferred unit of measurement (mm, cm, m, in, ft).
The calculator applies the formula V = (15 + 7√5) / 4 × a³.
The volume is displayed in the matching cubic unit.
Copy the result or try a different edge length.

Use cases

Calculate the volume of a dodecahedral die (D12) for game design.
Determine material volume when 3D-printing dodecahedral objects.
Verify geometric homework or exam answers instantly.
Estimate capacity of dodecahedron-shaped containers.
Explore the properties of Platonic solids in a math class.
Compare volumes of different Platonic solids at the same edge length.

Frequently Asked Questions

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