How to Calculate Regular Polygon
What is Regular Polygon?
A regular polygon calculator computes area, perimeter, interior and exterior angles, circumradius, and apothem for any regular polygon (equal sides and angles).
Formula
Interior angle = (n − 2) × 180 / n; Perimeter = n × side; Area = (n × side² × cot(180/n)) / 4
- n
- Number of sides
- s
- Side length (units)
- A
- Area (square units)
Step-by-Step Guide
- 1Area = (n × s²) / (4 × tan(π/n))
- 2Interior angle = (n−2) × 180° / n
- 3Exterior angle = 360° / n
- 4Circumradius R = s / (2sin(π/n)); Apothem a = s / (2tan(π/n))
Worked Examples
Input
Regular octagon, side 3cm
Result
Area = (8×9)/(4×tan(22.5°)) = 72/1.657 = 43.46 cm²; Interior angle = 135°
Frequently Asked Questions
What's the interior angle of a regular hexagon?
(6−2) × 180 / 6 = 720 / 6 = 120°.
Why is a circle considered a polygon with infinite sides?
As n increases, polygon approaches circle shape. Limit of regular n-gon as n→∞ = circle.
How many sides does a regular polygon need to look circular?
Visually, ~20+ sides looks very circular. Mathematically, infinite for true circle.
Ready to calculate? Try the free Regular Polygon Calculator
Try it yourself →