Annulus Area Calculator

About this calculator

An annulus is the flat ring-shaped region between two concentric circles — the same center, different radii. Its area is found by subtracting the smaller circle's area from the larger one's: π(R² − r²), where R is the outer radius and r is the inner radius; because both terms share the factor π, this can also be written as π(R − r)(R + r), which is handy when you know the ring's width and average radius rather than the two radii directly.

Annulus-area calculations are routine in mechanical engineering and manufacturing — washers, gaskets, pipe cross-sections, ball bearings and O-rings are all annular shapes, and knowing the enclosed area is necessary for stress calculations, flow-rate estimates through pipe walls, and material-quantity estimates when stamping parts from sheet stock. Architects and landscape designers also use the formula for circular walkways, fountains and garden rings built around a central circular feature.

This calculator takes the outer and inner radius of a ring and returns its exact area.