Annulus Calculator – Ring Area and Perimeter
Find the area, total boundary length and width of a circular ring from two concentric radii.
Formula
Area = π(R² − r²); perimeter = 2π(R + r); width = R − r
Outer radius R: 5 cm · Inner radius r: 3 cm · Ring area ≈ pi×((5 cm × 0.01 m/cm)-(3 cm × 0.01 m/cm))×((5 cm × 0.01 m/cm)+(3 cm × 0.01 m/cm))×10000 · Total boundary length ≈ 2×pi×((5 cm × 0.01 m/cm)+(3 cm × 0.01 m/cm))×100 · Ring width ≈ ((5 cm × 0.01 m/cm)-(3 cm × 0.01 m/cm))×100
How to use
- Enter the outer radius R.
- Enter the inner radius r in any offered length unit.
- Read area in cm² and lengths in cm.
Examples
- R = 5 cm and r = 3 cm give area 16π ≈ 50.265482 cm².
Frequently asked questions
Which radius must be larger?
R must be strictly greater than r; coincident radii do not form a ring with two distinct boundaries.
What does perimeter include?
It adds the outer and inner circumferences, including the hole boundary.
Can the inner radius be zero?
Yes. That limiting case is a filled disk. The circles must share a center.
Sources
Updated: