Case 1
- Edge length (not the circumradius)
- 3
206.904212
Open with these valuesRegular Dodecahedron Volume Calculator
206.904212units³
Result: 206.904212 units³All thirty edges of a regular dodecahedron are equal, so one edge fixes the whole solid: V = (15 + 7√5) ÷ 4 × a³, a factor of about 7.663119. An edge of 1 holds 7.663119 cubic units, an edge of 3 holds 206.904212. The surface area 3√(25 + 10√5) × a² stands in the table below.
Worked examples
Case 2
- Edge length (not the circumradius)
- 1
7.663119
Open with these valuesCase 3
- Edge length (not the circumradius)
- 5
957.889870
Open with these valuesHow it's calculated
V = (15 + 7√5) ÷ 4 × a³
- StepMeasure one edge — not the radius of the sphere around the solid.
- StepCube it and multiply by (15 + 7√5) ÷ 4 ≈ 7.663119.
- ResultRead the volume in the cube of the unit you entered.
Reference table
| Edge a | Exact volume | Surface area | Volume |
|---|---|---|---|
| 1 | (15 + 7√5) ÷ 4 | 20.645729 | 7.663119 |
| 2 | (15 + 7√5) × 8 ÷ 4 | 82.582915 | 61.304952 |
| 2.5 | (15 + 7√5) × 15.625 ÷ 4 | 129.035805 | 119.736234 |
| 3 | (15 + 7√5) × 27 ÷ 4 | 185.811559 | 206.904212 |
| 5 | (15 + 7√5) × 125 ÷ 4 | 516.143220 | 957.889870 |
Questions
How do I calculate the volume of a regular dodecahedron?
Cube the edge length and multiply by (15 + 7√5) ÷ 4, a factor of about 7.663119. For an edge of 3 that is 7.663119 × 27 ≈ 206.904212 cubic units.
What is a regular dodecahedron?
It is one of the five Platonic solids: twelve identical regular pentagons meeting at twenty vertices, with thirty equal edges. Because every edge is the same length, a single edge measurement fixes the whole shape. A d12 gaming die is a regular dodecahedron.
What is the surface area of a regular dodecahedron?
It is the total of twelve regular pentagons, 3 × √(25 + 10√5) × a², and the table above lists it for every example edge. For an edge of 3 that is about 185.811559 square units. Surface area scales with the square of the edge, so doubling the edge quadruples it.
Do I enter the edge or the radius?
The edge, meaning the length of one of the thirty straight sides. Radii of the inscribed, mid- and circumscribed sphere all lead to completely different formulas, so converting them first is on you.
How does a dodecahedron compare to a cube?
For the same edge length a dodecahedron holds far more. A cube of edge a has volume a³, the dodecahedron about 7.6631 × a³ — over seven and a half times as much, because it is the roundest of the Platonic solids.
Which units does the answer use?
Whatever you entered, cubed. An edge in centimetres gives cubic centimetres, an edge in inches cubic inches. The surface area in the table follows the same unit squared.
Sources and last check
Information, not professional advice.