Built and fact-checked by the DocNectar team — see our editorial standards
Key Features
Instant Calculation
Get accurate results in real time with our optimized algorithm.
Mobile Friendly
Fully responsive design. Works on all devices & screen sizes.
Privacy Focused
Your data stays on your device. We don't store any inputs.
100% Free
No hidden costs. This tool is completely free forever.
An annulus is the flat ring-shaped region between two concentric circles — like a washer or a donut cross-section — and its area is simply the difference between the two circles' areas.
This calculator finds an annulus's area, ring width, and both circumferences from its inner and outer radii.
How it works
Enter the outer and inner radii. The calculator subtracts the inner circle's area from the outer circle's area to find the ring's area, and also reports the ring's width and both circles' circumferences.
- Enter outer radius.
- Enter inner radius.
- Click Calculate to see your results.
Examples
Outer radius 10, inner radius 6
A ring with outer radius 10 and inner radius 6 has an area of about 201.06, a width of 4, an outer circumference of about 62.83, and an inner circumference of about 37.70.
Who should use it
- Calculating the area of a washer, gasket, or ring-shaped component for an engineering project.
- Checking geometry coursework involving the area between two concentric circles.
Industry applications
- Mechanical engineering and manufacturing (washers, gaskets, pipes)
- Geometry education
Advantages
- Reports area, width, and both circumferences together in one calculation.
- Uses the exact circle-area-subtraction formula, not an approximation.
Limitations
- Only handles a perfectly circular (concentric) ring — not elliptical or off-center ring shapes.
Common mistakes to avoid
- Confusing ring width (outer radius minus inner radius) with the ring's area, which are different measurements entirely.
- Entering an inner radius that's equal to or larger than the outer radius, which doesn't describe a valid ring shape.
Best practices
- Double-check that your outer radius is genuinely larger than your inner radius — the calculator will reject values where this isn't true, since they don't describe a real annulus.
Tips
- For a pipe's cross-sectional wall area (a very common real-world annulus), use the pipe's outer radius and inner radius (bore) directly — the result gives the actual material area in the pipe wall.