Area of Crescent Calculator
This calculator helps you to find the area for crescents and lunes. These shapes consists of two circular arcs and are determined based on their radii and the distance between the circle centers.
The formula
crescent = big circle − small circle (overlapping lunes)
A fully enclosed inner circle
When the smaller circle lies wholly inside the larger one, the crescent (or annulus, if the centres coincide) is simply the difference of the two areas — the offset does not change it. The offset only affects the shape: how thick the crescent is at each point. Once the circles overlap only partially the calculation needs circular segments instead, which is a different problem.
Area scales with the square
Double every length in a flat shape and the area quadruples; triple them and it grows ninefold. Perimeter, being a length, scales in step with the sides. That mismatch is why bigger shapes enclose proportionally more area per unit of edge — and why a circle, having no corners at all, encloses the most area for a given perimeter of any shape.
Units
Whatever unit you enter, the area comes out in that unit squared and the perimeter in the unit itself. The calculator is unit-agnostic — enter centimetres and read cm and cm², or feet and read ft and ft². Just do not mix units between fields.