An annulus is the ring-shaped region between two concentric circles — the same centre, two different radii. Real-world annuli include washers, the cross-section of a pipe, a circular path or track, and a CD. This calculator takes the outer and inner radius and returns the ring’s area, its width, and the circumference of both the outer and inner edges.
How it works
Let R be the outer radius and r the inner radius (the radius of the hole). The tool uses these standard formulas:
- Ring area = π(R² − r²) — the large circle’s area minus the small circle’s area.
- Ring width = R − r — the radial thickness of the band.
- Outer circumference = 2πR.
- Inner circumference = 2πr.
Enter both radii in the same unit and every result comes back in matching units (area in square units).
Example
A washer with an outer radius R = 10 mm and inner radius r = 6 mm:
- Area = π(10² − 6²) = π(100 − 36) = 64π ≈ 201.06 mm²
- Width = 10 − 6 = 4 mm
- Outer circumference = 2π × 10 ≈ 62.83 mm
- Inner circumference = 2π × 6 ≈ 37.70 mm
| Quantity | Formula | Result |
|---|---|---|
| Ring area | π(R² − r²) | 201.06 mm² |
| Ring width | R − r | 4 mm |
| Outer circumference | 2πR | 62.83 mm |
| Inner circumference | 2πr | 37.70 mm |
All calculations stay in your browser.