Dodecahedron Volume Calculator

Work out dodecahedron volume instantly with clear inputs, formula shown and shareable results.

About Dodecahedron Volume Calculator

A regular dodecahedron has twelve regular pentagonal faces. Its volume is ((15 + 7√5)/4)a³ ≈ 7.663119a³ and its surface area 3√(25 + 10√5)·a² ≈ 20.645729a².

Formulas

Volume

V = ((15 + 7√5)/4)·a³

Surface area

S = 3√(25 + 10√5)·a²

Worked example

With the default values below, Dodecahedron Volume Calculator returns Volume of 206.9042. Change any input above and every figure here is recalculated in your browser.

Inputs used

Edge lengthminimum 0: 3
Number of solidsminimum 1: 1

Results

Volume: 206.9042
Surface area (12 pentagons): 185.8116
Circumradius: 4.2038
Combined volume: 206.9042

Step by step

1Values used
2Volume
3Surface area
4Volume= 206.9042
5Surface area (12 pentagons)= 185.8116
6Circumradius= 4.2038
7Combined volume= 206.9042

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How many faces, edges and vertices?

Twelve faces, thirty edges and twenty vertices: 20 − 30 + 12 = 2.

Why does √5 appear?

Regular pentagons involve the golden ratio (1 + √5)/2, so √5 shows up throughout the dodecahedron's metrics.