Annulus (Ring) Area Calculator
Find the area of an annulus — the ring between two concentric circles — from the outer and inner radii.
How it works
Area = π(R² − r²), where R is the outer radius and r the inner radius
An annulus is the flat ring left when a smaller circle is removed from a larger concentric one — think of a washer or a CD. Its area is the big circle’s area minus the hole’s: π(R² − r²). Because that difference factors as π(R + r)(R − r), the ring’s area also equals its width (R − r) times the mean circumference π(R + r).
Worked example
With an outer radius of 5 and an inner radius of 3: area = π(5² − 3²) = π(25 − 9) = 16π ≈ 50.27 units². The ring is 5 − 3 = 2 units wide.
Sources: Annulus — Wolfram MathWorld
Frequently asked questions
What real objects are annuli?
Washers, flat rings, pipe cross-sections, CDs and the flat rim of a doughnut seen from above are all annuli — a disc with a concentric circular hole removed.
Can the inner radius be zero?
If the inner radius is zero there is no hole, and the annulus becomes a full disc of area πR². This calculator therefore requires the inner radius to be smaller than the outer one.
Related calculators
This calculator is for educational purposes. Double-check important results before acting on them.