Polycircle Calculator

Calculations at a polycircle. Here, a polycircle is a regular n-gon with a matching semicircle attached to each edge. A threecircle has the same shape as three circles, which intersect at their centers.
Enter the number of edges or semicircles and the edge length (circle diameter) and choose the number of decimal places. Then click Calculate.

	Number (n):			Example: fourcircle, n=4, base: square
	Edge length (a):
	Perimeter (p):
	Area (A):
	Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.

Lengths respectively circle diameter and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

This polycircle is axially symmetric about a number of axes equal to the number of semicircles or sides or corners of the inner polygon. For an even number n, there are two different types of axes of symmetry. One that runs centrally through two opposite semicircles and sides of the polygon, and one that runs through two opposite vertices of the polygon. For an odd number n, there is only one type of axis of symmetry, which runs centrally through a semicircle and the corresponding side of the polygon, and through the directly opposite vertex of the polygon. The polycircle is also point-symmetric about the intersection point of the symmetry axes. It is also rotationally symmetric about this point at an angle of 360°/n and multiples thereof.
With an increasing number of sides, the size of the semicircles becomes smaller relative to the size of the inner polygon, and the polycircle, like the regular polygon, increasingly approaches a circle.
The shape of the polycircle is reminiscent of a flower with rather short petals. For other flower shapes, see epicycloid and rose.

Last updated on 04/01/2026. Author: Jürgen Kummer

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