Enter the outer radius and inner radius of two concentric circles to calculate the annulus area, along with the outer and inner circumferences and individual circle areas. The Annulus Calculator gives you all five geometric properties of a ring-shaped region — just plug in your two radii and see the full breakdown.
Annulus Area (A₀)
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Outer Circle Area (A₁)
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Inner Circle Area (A₂)
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Outer Circumference (C₁)
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Inner Circumference (C₂)
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Ring Width (r₁ − r₂)
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An annulus is the region (ring-shaped area) between two concentric circles — meaning two circles that share the same center point. Think of it like a washer, a donut cross-section, or a circular garden border. The area of the annulus is the area of the outer circle minus the area of the inner circle.
The area of an annulus is calculated as A₀ = π(r₁² − r₂²), where r₁ is the outer radius and r₂ is the inner radius. This is equivalent to subtracting the inner circle's area (A₂ = πr₂²) from the outer circle's area (A₁ = πr₁²).
The outer circumference is C₁ = 2πr₁ and the inner circumference is C₂ = 2πr₂. These measure the perimeter of the outer and inner boundary circles of the annulus, respectively.
No — the inner radius must always be smaller than the outer radius. If the inner radius equals or exceeds the outer radius, the annulus has zero or negative area, which is geometrically meaningless. This calculator will flag that condition and prompt you to correct your inputs.
The ring width (sometimes called the width of the annulus) is simply the difference between the outer and inner radii: w = r₁ − r₂. It represents how wide the ring-shaped region is from its inner edge to its outer edge.
Annuli appear frequently in everyday life and engineering. Common examples include washers (the flat ring used with nuts and bolts), cross-sections of pipes and tubes, circular garden borders or flower beds around a central feature, optical lenses, and the face of many mechanical gears and pulleys.
The annulus area A₀ equals the outer circle area A₁ minus the inner circle area A₂. So A₀ = A₁ − A₂ = π(r₁² − r₂²). The outer circle completely contains both the inner circle and the ring-shaped annulus region.
You can select any unit of length (mm, cm, m, km, in, ft, yd, or mi) from the dropdown. The area result will be in square units of your chosen measurement (e.g. m²), and circumferences will be in the same linear unit. The calculator does not convert between units — just enter your values in a consistent unit.