Regular Polygon Calculator for Area, Perimeter, Apothem and Angles

Updated By Unit Conversion Plus

Solve any regular polygon from its number of sides and one known measurement.

Polygon measurements

What is a regular polygon?

A regular polygon has equal side lengths and equal interior angles. Examples include equilateral triangles, squares, regular pentagons, hexagons and octagons.

Regular polygon formulas

P = ns · A = ns² ÷ (4 tan(π/n)) · a = s ÷ (2 tan(π/n)) · R = s ÷ (2 sin(π/n))

Angles and diagonals

Each interior angle is (n − 2) × 180° ÷ n, each exterior angle is 360° ÷ n, and the polygon has n(n − 3) ÷ 2 diagonals.

Frequently asked questions

Does this work for irregular polygons?

No. The formulas assume every side and interior angle is equal.

What is an apothem?

It is the perpendicular distance from the polygon's centre to the midpoint of a side.