Ring / Annulus Area Calculator

Calculate the area of a ring (annulus) — the space between two concentric circles. Enter outer and inner radius for instant results.

Annulus Calculator
Annulus Area
160.22
sq ft
Outer Circle
314.16
sq ft
Inner Circle
153.94
sq ft

What is Ring / Annulus Area Calculator?

An annulus area calculator computes the area of a ring — the flat region between two concentric circles (circles that share the same center). The annulus is the "donut" shape you see in washers, pipe cross-sections, circular walkways around ponds, and running tracks.

This tool exists because calculating a ring area requires subtracting one circle area from another. While the formula is straightforward (π(R² − r²)), it is easy to make arithmetic errors with π and squaring. The calculator gives you instant, accurate results for any radius values.

Ring / Annulus Area Calculator Formula

Area = π × (R² − r²)

Where R is the outer radius and r is the inner radius. This formula works because the annulus area equals the outer circle area (πR²) minus the inner circle area (πr²).

Example: Outer radius = 10 ft, inner radius = 7 ft. Area = π × (10² − 7²) = π × (100 − 49) = π × 51 = 160.22 sq ft.

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Frequently Asked Questions

What is an annulus?
An annulus is the region between two concentric circles — a ring shape. It looks like a donut or washer. The area equals the outer circle area minus the inner circle area: A = π(R² − r²), where R is the outer radius and r is the inner radius.
How do I calculate the area of a ring?
Measure the outer radius (R) and inner radius (r). Use the formula A = π(R² − r²). For a ring with outer radius 10 ft and inner radius 7 ft: A = π(100 − 49) = π × 51 = 160.22 sq ft.
What is the difference between annulus area and ring area?
They are the same thing. 'Annulus' is the mathematical term, and 'ring' is the common name. Both refer to the area between two concentric circles.
Can I use the annulus formula for pipes?
Yes. The cross-sectional area of a pipe wall is an annulus. Use the outer diameter and inner diameter (divide each by 2 for radius). This gives the material area of the pipe cross-section.
How do I calculate annulus area from diameters?
Divide each diameter by 2 to get the radii, then use A = π(R² − r²). For outer diameter 20 ft and inner diameter 14 ft: R = 10, r = 7, A = π(100 − 49) = 160.22 sq ft.