Regular Polygon Calculator

About this calculator

This calculator finds the perimeter, P = n·s, and area, A = (1/4)·n·s²·cot(π/n), of any regular polygon from its number of sides n and side length s, where the area formula comes from splitting the polygon into n congruent isosceles triangles meeting at the center and using the cotangent of the half-angle at the apex. This generalizes the familiar formulas for squares, pentagons, and hexagons into a single equation that works for any number of sides.

Architects and land surveyors use it when laying out regular-shaped plots, gazebos, or plaza tiles, and CAD and graphics developers use the same geometry when generating polygon shapes programmatically. Geometry and trigonometry students use this calculator to check homework involving pentagons, hexagons, or higher-order polygons, and game developers building tile-based or procedurally generated environments use it to compute exact polygon dimensions.