Regular Polygon Area Calculator

About this calculator

This tool calculates the area and perimeter of a regular polygon — a shape where all sides and all interior angles are equal, like a regular pentagon or hexagon — from just the number of sides and the length of one side. It uses the standard formula that relates a regular polygon's area to its number of sides, side length, and the apothem (the distance from the center to the midpoint of a side), a relationship that generalizes the familiar area formulas for squares and equilateral triangles to any number of sides.

It is used by students verifying geometry homework involving polygons beyond the basic triangle and square cases, and by people in practical design or construction contexts — laying out a hexagonal tile pattern, cutting a pentagonal sign, or estimating material for an octagonal deck or gazebo — who need the area or perimeter of a many-sided shape without deriving the formula from scratch each time.