Annulus Calculator

Calculations at an annulus (circular ring). An annulus is made of two concentric circles of different size. The smaller circle is subtracted from the larger.
Enter at radiuses and breadth two values and choose the number of decimal places. Then click Calculate.

	Radius of the large circle (R):
	Radius of the small circle (r):
	Breadth (b):
	Longest interval (l):
	Perimeter (p):
	Area (A):
	Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.

Radius, breadth, length and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter). Perimeter refers to inner and outer boundary lines.

Here, the perimeter is defined as the circumference of the outer circle plus that of the inner circle. For the perimeter and surface area, it is irrelevant whether the inner ring is removed in the middle or offset, as long as it does not intersect the outer ring. In the case of intersecting, lunes are created. For the longest interval and other properties, however, the position of the inner circle does play a role; here it is assumed that it is removed from the middle. This is what is meant by the term concentric, both circles have a common center.
An annulus halved in the middle is a semi-annulus. Parts of a circular ring are a annulus sector if the division starts from the center and a annulus segment if it is divided by a straight line. If the ring is formed by ellipses instead of circles, then it is an elliptical ring. A remotely similar object is the cash shape. The three-dimensional equivalent of the circular ring is the spherical shell; a straight extension into the third dimension leads to the cylindrical shell.
The annulus has the same symmetry properties as the circle. It is point-symmetrical to the center, axially symmetrical to any straight line through it and rotationally symmetrical to a rotation through any angle.

Last updated on 06/04/2026. Author: Jürgen Kummer

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