Annulus Area
Calculator

An annulus is a flat ring shape, the region between two concentric circles (circles sharing the same center) of different radii. Its area is A = π(R² − r²), where R is the outer radius and r is the inner radius, simply the outer circle's area minus the inner circle's area.

Area scales with the square of radius, not radius itself, so you must calculate each circle's full area separately (using r²) before subtracting; subtracting the radii first and then squaring would give a completely different and incorrect number. This is a very common calculation mistake with ring-shaped objects like washers or pipes.

Yes, since π(R²−r²) factors as π(R+r)(R−r), and if you know the ring's width w = R−r, you can rewrite the area as πw(R+r), or equivalently 2π·w·r_mean, where r_mean is the average of the two radii. This alternate form is sometimes more convenient depending on which measurements you have.

Yes, but you must convert diameters to radii first (dividing each by 2) before applying the formula, since the standard formula is defined in terms of radii, not diameters. Plugging diameters directly into π(R²−r²) without halving them first would overestimate the area by a factor of 4.

Washers, gaskets, pipe cross-sections, and CDs/records are all annulus-shaped, and this formula directly gives the material area needed, useful for calculating material cost, weight, or flow area through a pipe. It's one of the more practically common area formulas in engineering and manufacturing contexts.