Regular Polygon Calculator
Calculate area, perimeter, apothem and angles of any regular polygon given sides and length.
Inputs
units
Area
90.8478sq units
Perimeter
35.0000units
Apothem
5.1913units
Circumradius
5.7619units
Interior Angle
128.5714°
Exterior Angle
51.4286°
Step by step
Interior angle
(7−2)×180/7
= 128.5714°
Apothem
a = 5 / (2×tan(π/7))
= 5.1913
Area
A = ½ × 35 × 5.1913
= 90.8478
How it works
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
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.