An annulus is the flat region between two concentric circles (circles sharing the same center). Common real-world examples include washers, rings, and the cross-section of a hollow cylinder.

What formula does this use?

A = π(R² − r²), where R is the outer radius and r is the inner radius. This is equivalent to subtracting the area of the inner circle from the area of the outer circle.

What if the inner radius equals the outer radius?

If R = r the annulus has zero area — it collapses to a single circle with no width. The tool will show 0.

Can the inner radius be larger than the outer radius?

No. The inner radius cannot be larger than the outer radius. If you enter r > R the tool shows an inline error.

Does the unit affect the formula?

The unit label changes the display only. The math is the same regardless of unit — just make sure both radii use the same unit.

How precise are the results?

Results are shown to 6 significant figures using JavaScript's built-in Math.PI constant (≈ 3.141592653589793).

Area of an Annulus Calculator

Enter the outer and inner radii to instantly compute the area of an annulus using A = π(R² − r²).

Annulus Dimensions

Outer Radius (R)

Inner Radius (r)

Unit

Annulus Diagram

Area (A)

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A = π × (R² − r²)

Summary

An annulus is the region between two concentric circles — like a washer, a ring, or a donut cross-section. This calculator uses the formula A = π(R² − r²), where R is the outer radius and r is the inner radius, to give you the exact area in any unit you choose. Results update instantly as you type.

How it works

Enter the outer radius (R) — the distance from the center to the outer edge.
Enter the inner radius (r) — the distance from the center to the inner edge.
Choose the unit of measurement (mm, cm, m, in, ft).
The calculator applies A = π(R² − r²) and displays the result instantly.
Copy the result or swap the unit without re-entering values.

Use cases

Calculate material needed to cut a washer or gasket.
Find the cross-sectional area of a hollow pipe or tube.
Determine paint or flooring coverage for ring-shaped surfaces.
Verify engineering drawings involving circular cutouts.
Solve geometry homework involving concentric circles.
Estimate annular area in optical or lens design.

Frequently Asked Questions

Last updated: 2026-05-23 · Reviewed by Nham Vu