Polygon Apothem Calculator

About this calculator

The apothem of a regular polygon is the perpendicular distance from its center to the midpoint of any side, calculated as a = s / (2·tan(π/n)), where s is the side length and n is the number of sides. Once known, the apothem gives the polygon's area directly via A = ½ × perimeter × apothem — the same logic used to derive a circle's area as a limiting case when n grows very large.

Architects and structural engineers use the apothem when designing polygonal structures like gazebos, pavilions, or geodesic elements, machinists and fabricators use it for CNC and laser-cutting layouts of hexagonal or octagonal parts (including standard hex bolt heads and nuts), and game and graphics developers use it when rendering or generating regular polygons procedurally. Geometry students also use it as a standard tool for computing polygon area without needing to break the shape into triangles by hand.