Icosahedron Calculator
What are the volume and surface area of a regular icosahedron? Enter the values below to calculate the result.
Result for the values shown.
Calculations run in your browser.
What to enter
| Input | Meaning and units |
|---|---|
| Side a (length) | Enter side a in length; use the same basis as the other measurements. |
Understanding your result
Read volume (length^3), surface (length^2) in the units and model stated on this page. The formula volume=5*(3+sqrt(5))*a^3/12 · surface=5*sqrt(3)*a^2 defines the relationship; measurement accuracy and model applicability are separate from numerical precision.
Common mistakes
- Mixing input units or changing the physical meaning of a variable without changing the model.
Check your calculation
- Use the worked example as a known reference case, then change one input at a time and check the direction and units of the response.
Calculation checks, sources and review limits
What are the volume and surface area of a regular icosahedron?
What are the volume and surface area of a regular icosahedron? Enter the values below to calculate the result.
Common uses
- What are the volume and surface area of a regular icosahedron
How it works
volume=5*(3+sqrt(5))*a^3/12; surface=5*sqrt(3)*a^2
Worked example
Enter Side a: 1 length. Results: volume: 2.1816949906249126 length^3; surface: 8.660254037844386 length^2.