Pentagon formulas
A regular pentagon has five equal sides and internal angles of 108 degrees. The diagonal-to-side ratio equals the golden ratio (1 + sqrt(5))/2 ≈ 1.618.
Area = (s^2 * sqrt(25 + 10*sqrt(5))) / 4. Perimeter = 5s.
Pentagon Calculator
Calculate area, perimeter, diagonal, inradius, and circumradius of a regular pentagon from side length.
Share this calculator
Result
61.94 area
Total area of a regular pentagon with side length 6.
- Perimeter
- 30
- Circumradius
- 5.1
- Inradius
- 4.13
- Diagonal
- 9.71
About the diagonal
The diagonal of a regular pentagon equals the side length multiplied by the golden ratio (1.618...), connecting the deep relationship between pentagons and the golden ratio.
Also in General
Geometry
Regular pentagon properties from side length
The pentagon calculator computes area, perimeter, diagonal, inradius, and circumradius of a regular pentagon from its side length.
Limitations
This calculator handles regular pentagons only.
Frequently asked questions
In a regular pentagon, the diagonal divided by the side length equals the golden ratio phi ≈ 1.618. This makes pentagons fundamental to golden-ratio geometry.
108 degrees. (5-2) * 180 / 5 = 108.
Related
More from nearby categories
These related calculators come from the same leaf category, nearby sibling categories, or the same top-level topic.
Hexagon Calculator
Calculate area, perimeter, diagonals, inradius, and circumradius of a regular hexagon from side length.
Open calculator
Octagon Calculator
Calculate area, perimeter, diagonals, inradius, and circumradius of a regular octagon from side length.
Open calculator
Polygon Calculator
Calculate area, perimeter, interior and exterior angles, and diagonal count for any regular polygon.
Open calculator
Rhombus Calculator
Calculate area, perimeter, diagonals, and angles of a rhombus from side and angle or diagonal inputs.
Open calculator