Annulus (Ring) Area Calculator

An annulus is the flat ring left between two circles that share the same centre. A metal washer, a CD, and a doughnut seen from directly above are all familiar examples of the shape.

The area equals pi times the outer radius squared minus the inner radius squared. It is simply the area of the large disc minus the area of the hole punched out of its middle, so area = pi (R squared - r squared).

The width is the outer radius minus the inner radius, the straight distance across the solid band from the inner edge to the outer edge. For an outer radius of 5 and an inner radius of 3 the width is 2.

An annulus has two boundaries, so it has two circumferences: the outer one is 2 times pi times the outer radius, and the inner one is 2 times pi times the inner radius. Both are useful when the ring is a physical part with an inside and an outside edge.

If the outer radius were equal to or smaller than the inner radius there would be no ring, only a line or an empty shape. The tool requires the outer radius to be strictly greater than the inner radius, and the inner radius itself must be greater than zero.

Yes. Both fields accept decimals, and the results are rounded to six decimal places. Values must be finite numbers; an inner radius of zero or an outer radius that is not larger than the inner one produces a short error instead of a result.

It is unit free. Enter both radii in the same unit, and the area comes out in the corresponding square unit while the width and both circumferences are in the same length unit you entered.

Divide each diameter by two first, since the radius is half the diameter. A ring with an outer diameter of 10 and an inner diameter of 6 has an outer radius of 5 and an inner radius of 3.

Yes. The calculation runs entirely in your browser as you type, so no measurements are uploaded or stored anywhere.