Polygon Circumradius Calculator

About this calculator

For a regular polygon with n sides of length s, this calculator finds the circumradius R = s / (2 sin(π/n)) — the distance from the center to each vertex — and the inradius (apothem) r = s / (2 tan(π/n)), the distance from the center to the middle of each side. Both come from splitting the polygon into n identical isosceles triangles with a central angle of 2π/n.

Architects and carpenters use the circumradius to lay out gazebos, pavilions, and cupolas on a circular foundation, machinists use it to space bolt holes evenly on a bolt-circle pattern, and manufacturers of nuts and hex stock use the inradius (the wrench-flat distance) to check part dimensions against the circumradius (the corner-to-corner distance).