Annulus (Ring) Area Calculator
Find the area of an annulus (ring) from its outer and inner radius or diameter, plus ring width, both circumferences and the area of a ring sector.
An annulus is the flat ring between two circles that share a centre, like a washer, a pipe’s cross-section, a running track or the border of a round garden bed. This calculator gives its area from the outer and inner radius or diameter, along with the ring width and both circumferences. Enter a sector angle below 360° to get the area and edge lengths of just a slice of the ring.
How to use this tool
- Choose whether you are entering radii or diameters.
- Enter the outer and inner sizes and pick a unit.
- Leave the angle at 360° for a full ring, or enter a smaller angle for a ring sector.
- Read the area, ring width and circumferences (or arc lengths for a sector).
Formula
A = π (R² − r²)
R is the outer radius and r the inner radius (half the diameters). The same area can be written as A = π (R + r)(R − r) = 2π × mean radius × width. For a sector of angle θ, multiply the area and each circumference by θ / 360.
Example
A washer has an outer radius of 10 cm and a hole of radius 6 cm. Its area is π × (10² − 6²) = π × 64 ≈ 201.06 cm². The ring is 4 cm wide, the outer edge is 2π × 10 ≈ 62.83 cm long and the inner edge 2π × 6 ≈ 37.70 cm, and the ring covers 64% of the full 10 cm circle.
Frequently asked questions
How do I find the area of a ring from its width?
If you know the outer radius R and the width w, the inner radius is r = R − w. Enter those two radii, or use A = π w (2R − w).
Does the area depend on the units?
Only in the label. Enter both sizes in the same unit and the area comes out in that unit squared, for example cm².
What is a ring sector?
It is the part of the annulus between two radii, like a curved tile or a section of a circular path. Its area is the full ring area × angle / 360.
Can the inner radius be zero?
Yes. Then the annulus is a full disc and the area is simply πR².
Last updated: 2026-10-30