Annulus Calculator
Calculate the area of an annulus (ring or washer shape) formed by two concentric circles. Formula: Area = π(R² - r²).
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Frequently Asked Questions
What is an annulus?
An annulus is a ring-shaped region bounded by two concentric circles (circles with the same center). It looks like a washer or donut shape.
What is the formula for annulus area?
Area = π(R² - r²), where R is the outer radius and r is the inner radius. This equals the outer circle's area minus the inner circle's area.
Can the inner radius be zero?
Yes, if r = 0, the annulus becomes a full circle with area πR². The annulus formula still works correctly in this case.
What if the radii are equal?
If R = r, the area is zero because there's no ring. The inner radius must be less than the outer radius for a valid annulus.
What is the width of an annulus?
The width (or thickness) of the ring is w = R - r, the difference between the outer and inner radii.
What are real-world examples of annuli?
Washers, gaskets, rings, circular tracks, pipe cross-sections, and CD/DVD surfaces are all annular shapes.
How do you calculate annulus area from width?
If you know R and width w, then r = R - w. Substitute into the formula: Area = π(R² - (R-w)²) = π(2Rw - w²).
Where are annulus calculations used?
Annulus calculations are used in engineering (pipe sizing, washers), manufacturing, architecture (circular windows with frames), and astronomy (planetary rings).