Reuleaux Triangle Area Calculator

About this calculator

A Reuleaux triangle is built by taking an equilateral triangle and replacing each straight side with a circular arc centered on the opposite vertex, using the triangle’s side length as the radius. The result is a curved shape with rounded corners that has constant width — like a circle, its width is the same no matter which direction you measure it — even though it clearly isn’t round.

That constant-width property is why Reuleaux triangles show up in real engineering: the Wankel rotary engine’s rotor is shaped like one, Watts Brothers-style drill bits use the shape to bore (almost) square holes, and some coin shapes and manhole cover designs use the same principle so the shape can’t fall through its own opening at any rotation. For a given width w, its area is (π − √3) × w² / 2 and its perimeter equals π × w — the same perimeter formula as a circle of diameter w, since it’s made of three arcs each spanning 60° of a circle with that radius. This calculator takes the width and returns both the area and perimeter.