Annulus Area Calculator — Area Between Two Circles

Real-world use cases

• Size the seating face of a flat washer

  You are picking washers for a bolted joint and need the contact area that spreads the clamping load. A washer is a metal annulus: outer radius R, bolt-hole radius r. Enter both and read π(R² − r²) directly. A washer 20 mm across the outside with an 8 mm hole has R = 10 and r = 4, a seating face of π(100 − 16) ≈ 263.9 mm². Compare two washer sizes side by side and pick the one that keeps the pressure under the material limit.

• Find a pipe wall cross-section for flow or material

  The cross-section of a pipe wall is an annulus between the outer and inner radii, and it drives both how much steel the pipe contains and how it carries axial load. Halve the outer and inner diameters into R and r, enter them, and the area is your wall cross-section. The same run also gives the inner circumference, handy when you need the inside surface for lining or flow estimates.

• Lay out a running-track lane or a circular path

  A track lane, a circular walking path, or a donut-shaped flower bed is an annulus between two radii. Enter the outer and inner radii to get the paved or planted area so you can order gravel, turf or soil by the square metre. The ring width R − r tells you how wide the lane or path actually is, which is the number a contractor asks for first.

• Solve the inner radius for a target ring area

  Sometimes the area is the requirement, not the result. You want a ring-shaped seal with a fixed outer radius that covers a specific face area. Switch to solve mode, fix R, type the area, and the tool back-solves r = √(R² − A∕π). It refuses politely if the area you ask for is bigger than the full outer disc, since no inner circle could leave that much ring.

Common pitfalls

• Entering diameters where the tool expects radii. A diameter is twice the radius, so a 10 cm outer diameter is R = 5, not 10. Forgetting to halve doubles every length and inflates the area by a factor of four. The tool keeps a reminder by the inputs.

• Putting the larger value in the inner field. The inner radius must be smaller than the outer one, otherwise R² − r² goes negative and no ring exists. If you swap them the tool shows a range message instead of a result — check which field is which before reading the number.

• Asking for a target area bigger than the full outer disc in solve mode. The most ring you can ever get from radius R is the whole disc πR², reached when the inner radius is 0. Request more than that and there is no valid inner radius, so the tool flags it rather than inventing one.

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