Annulus (Ring) Area Calculator

How it is calculated

Area is A = π × (R² − r²) and total edge length is P = 2π × (R + r), where R is the outer radius and r the inner radius, both in the same length unit. Area comes out in that unit squared, perimeter in that unit. The perimeter is the outer circle plus the inner circle, which is the length of both edges of the ring.

The tool returns no result if the outer radius is zero or negative, the inner radius is negative, or the inner radius is equal to or larger than the outer one. An inner radius of 0 is allowed and gives a plain disc. Results are rounded to two decimals. It takes radii, not diameters.

Common mistakes

• Entering diameters. A 20 cm outer and 12 cm inner measurement must be halved to 10 and 6 first, or the area is four times too large.
• Subtracting the radii first, π × (R − r)². The correct formula subtracts the squares, R² − r²; (10 − 6)² is 16 but 100 − 36 is 64.
• Putting the radii in the wrong boxes. If the inner value is not smaller than the outer one, the tool gives no result.
• Mixing units, such as a pipe outer size in millimetres and the wall in centimetres. Convert both radii to one unit first.
• Expecting the perimeter to be the area of the edge. It is only the combined length of the two circles; a pipe's cut face needs the area, not the perimeter.