Annulus (Ring) Area Calculator
Calculate the area of an annulus (ring shape) from its outer and inner radii. Formula: Area = pi x (R^2 - r^2). Instant and accurate.
How to use this tool
- Enter outer radius (r) and inner radius (r) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your annulus area and the full breakdown beneath it.
Formula
Area = pi x (R^2 - r^2)
How it works
An annulus is the region between two concentric circles. Subtract the inner circle area from the outer circle area: pi x R^2 - pi x r^2 = pi x (R^2 - r^2).
Worked example
Annulus with outer radius 8 m and inner radius 5 m
- Outer area = pi x 8^2 = 64 x pi = 201.0619 m^2
- Inner area = pi x 5^2 = 25 x pi = 78.5398 m^2
- Annulus area = 201.0619 - 78.5398 = 122.5221 m^2
122.5221 m^2
Common mistakes to avoid
- Subtracting the radii before squaring as (R-r)^2 instead of squaring each radius first and then subtracting R^2 - r^2.
- Entering the inner and outer diameters instead of radii; halve each diameter before entering.
- Entering a larger value for r than for R, producing a negative result; the outer radius R must always exceed the inner radius r.
Key terms
- What is an annulus?
- The region between two concentric circles (a ring or washer shape).
- Does the inner radius matter much?
- Yes. A larger inner radius means a thinner ring and much less area.
Frequently asked questions
- What is an annulus?
- An annulus is the region between two concentric circles sharing the same center. It looks like a flat ring or washer.
- Can I use the formula if I know the ring width instead of the inner radius?
- Yes. If width w = R - r, then r = R - w. Substitute to get the inner radius, then enter both R and r.
- How is the annulus area related to the areas of the two individual circles?
- Annulus Area = pi x R^2 - pi x r^2 = pi x (R^2 - r^2). The formula comes directly from that subtraction.