Regular Dodecahedron Calculator
From one edge length, get the volume and the total surface area — the two numbers that describe any regular dodecahedron.
One input, two answers
Enter the edge length and the calculator returns the volume (((15+7√5)/4)·a³) and the surface area (3√(25+10√5)·a²) at once.
Keep units consistent
The edge length is unit-agnostic — your answers come back in the same unit (squared for the surface, cubed for the volume), so don't mix centimetres with inches.
What is a regular dodecahedron calculator?
One edge in, full solid out
A regular dodecahedron is one of the five Platonic solids: twelve identical regular-pentagon faces meeting at twenty vertices, with thirty equal edges. Because every edge is the same length, a single measurement — the edge length a — fixes the entire shape. This calculator turns that one number into the volume (how much it holds) and the total surface area (all twelve pentagons). It is the tool for d12 gaming dice, pyrite crystals, geometric models, and any geometry homework where a regular dodecahedron shows up.
Enter the edge length in any length unit to get the volume and surface area instantly.
Two formulas, both built from the single edge length a and the square root of 5 (≈ 2.23607).
volume = ((15 + 7√5) / 4) × a³The surface area is the total of twelve regular-pentagon faces, which adds up to 3 × √(25 + 10√5) × a². The volume, the space inside, is ((15 + 7√5) / 4) × a³: the factor (15 + 7√5)/4 is about 7.6631, so a dodecahedron holds roughly seven and a half times the cube of its edge — far more than a cube of the same edge.
Suppose you have a regular dodecahedron with an edge length of 3.
Surface area
3 × √(25 + 10√5) × 3² = 3 × √(25 + 10√5) × 9 = 185.811559 square units — all twelve pentagons.
Volume
((15 + 7√5) / 4) × 3³ = ((15 + 7√5) / 4) × 27 = 206.904212 cubic units — the space inside.
The two outputs answer two different questions. The volume (about 206.904212 cubic units for a = 3) is how much the solid holds — useful for a crystal, a model, or a packing estimate. The single most useful insight is that the volume factor (15 + 7√5)/4 ≈ 7.6631 is large: a dodecahedron is the roundest of the Platonic solids, so for a given edge it encloses far more space than a cube (which holds only a³ = 1 × edge cubed). The surface area (about 185.811559 square units) is the total of all twelve pentagons — what you would paint or coat, and it scales with the square of the edge, so doubling the edge quadruples the surface while the volume grows eightfold. Because both quantities grow from the same single edge, scaling the model up or down is just a matter of rescaling a, and the dodecahedron's high symmetry means it has no special "top" or "front" to worry about.
The formulas are exact, but a couple of practical points are worth keeping in mind.
Regular dodecahedra and consistent units
These formulas describe a perfect regular dodecahedron — twelve identical regular-pentagon faces with every edge the same length. A non-regular or irregular twelve-faced solid (a dodecahedron whose faces or edges differ in size) does not follow these formulas. The edge length is also unit-agnostic, so the answers are only meaningful if you keep one unit throughout: an edge in centimetres gives a volume in cubic centimetres and a surface area in square centimetres, never a mix.