Regular Polygon Calculator
Calculate area, perimeter, apothem and angles of any regular polygon given sides and length.
About Regular Polygon Calculator
A regular polygon has n equal sides and n equal angles. Area = ½ × perimeter × apothem. Interior angle = (n−2)×180°/n.
Formulas
Interior Angle
θ = (n−2) × 180° / n
- n
- Number of sides
Area
A = ½ × n × s × apothem
- n
- Number of sides
- s
- Side length
- a
- Apothem
Worked example
With the default values below, Regular Polygon Calculator returns Area of 90.8478. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Number of Sidesminimum 3
- 7
- Side Lengthminimum 0 units
- 5 units
Results
- Area
- 90.8478 sq units
- Perimeter
- 35.0000 units
- Apothem
- 5.1913 units
- Circumradius
- 5.7619 units
- Interior Angle
- 128.5714 °
- Exterior Angle
- 51.4286 °
Step by step
- 1Interior angle= 128.5714°
- 2Apothem= 5.1913
- 3Area= 90.8478
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
What happens as n increases?
The polygon approaches a circle. As n → ∞, the area approaches πr² and the perimeter approaches 2πr.
What is the exterior angle sum for any polygon?
The exterior angles always sum to 360° for any convex polygon.