Annulus calculator
This annulus calculator works from the outer and inner radius, from both diameters, or from the area and outer radius. With R = 5 and r = 3 the area is 50.27 and the ring width 2, with the full calculation steps.
Example: Known values: Outer and inner radius · Outer radius R 5 · Inner radius r 3 → Result: Area A = 50.26548. Source: Wikipedia – Kreisring. Updated: .
How it is calculated
An annulus is the region between two circles that share the same centre. You get it by cutting a smaller circle (radius r) out of a larger one (radius R), like a washer or the cross-section of a pipe.
The formulas
- Area: A = π · (R² − r²) = π · (R + r) · (R − r)
- Ring width: b = R − r
- Outer circumference: C = 2 · π · R, inner circumference: 2 · π · r
- With diameters: A = π ÷ 4 · (D² − d²)
- Inner radius from the area: r = √(R² − A ÷ π)
How to use it
Choose the known measures and enter the values. Example: R = 5 and r = 3 give A = π · (25 − 9) = 50.27, a ring width of b = 2 and circumferences of 31.42 and 18.85. The inner circle must be smaller than the outer one. The unit is up to you; the area is in the square of the chosen unit.
Frequently asked questions
How do you calculate the area of an annulus?
A = π · (R² − r²): the area of the large circle minus the area of the small one. For R = 5 and r = 3 that is π · 16 = 50.27.
How do you calculate an annulus from diameters?
A = π ÷ 4 · (D² − d²). Choose “Outer and inner diameter”; the tool halves the values for you.
How do you find the inner radius from the area?
r = √(R² − A ÷ π). The area must be smaller than π · R², otherwise there would be no hole left.
What is the ring width?
The distance between the outer and inner circle, b = R − r. For R = 5 and r = 3 it is 2.
What is an annulus used for?
For example washers, pipe cross-sections, gaskets, or the area of a path around a round pond.
Sources and legal basis
As of: · Editorial policy
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