Triangle Circumradius Calculator

About this calculator

The circumradius of a triangle — the radius of the unique circle passing through all three vertices — can be found from the three side lengths as R = abc/(4·Area), where Area comes from Heron's formula, or equivalently from the law of sines as R = a/(2·sin A) using any side and its opposite angle. Every triangle has exactly one circumscribed circle, whose centre (the circumcenter) is the intersection of the perpendicular bisectors of the sides.

This relation is central to trigonometry coursework and to any application that needs a circle fitted exactly through three points: surveyors and civil engineers use it to lay out curved roads and arcs from three known points, machinists and CNC programmers use it to compute bolt-circle or fillet radii, and computational-geometry and computer-graphics code uses it for triangle mesh analysis and Delaunay triangulation.