Annulus Area Calculator

How it is calculated

An annulus is the flat ring between two circles that share a centre. Its area is the area of the big disc minus the area of the hole: A = π × R² − π × r² = π × (R² − r²), where R is the outer radius and r the inner radius. Both are radii, measured from the centre, not diameters.

The tool has no unit setting. Enter both radii in the same unit and the result is in that unit squared; the answer is labelled "units²" and shown to two decimals. The outer radius must be above zero, the inner radius cannot be negative and must be smaller than the outer radius, otherwise there is no result. An inner radius of 0 is accepted and simply returns the area of the full circle, π × R².

Common mistakes

• Entering diameters instead of radii. A pipe with an outside diameter of 20 has R = 10, so halve the diameters first.
• Subtracting the radii before squaring, for example π × (R − r)². The radii are squared first, then subtracted.
• Putting the inner value in the outer field. The inner radius must be smaller, otherwise the tool returns nothing.
• Mixing units, such as an outer radius in cm and an inner one in mm.
• Reading the answer as a length. It is an area, in the square of whatever unit you used, even though the label only says "units²".