Annulus (Ring) Calculator
The Annulus (Ring) Calculator finds the area, circumferences, and width of a ring — the region between two concentric circles. Enter the outer and inner radii and it returns all the key measurements of the ring. The formulas used are: area = π(R² − r²); outer circumference = 2πR; inner circumference = 2πr; width = R − r.
Formula
Area = π(R²−r²); Outer circumference = 2πR; Inner circumference = 2πr; Width = R−r
- The Annulus (Ring) Calculator updates instantly when you change either radius.
- Formula: Area = π(R² − r²); Outer circumference = 2πR; Inner circumference = 2πr; Width = R − r
- Input definitions: • Outer Radius R: radius of the outer circle • Inner Radius r: radius of the inner (hole) circle, which must be smaller than R
- The area is simply the big circle's area minus the small circle's area.
- Average radius (R + r) ÷ 2 is the radius of the centreline of the ring.
- Keep both radii in the same unit; the area comes out in that unit squared.
Example Calculation
Inputs
- Outer Radius R (cm): 10
- Inner Radius r (cm): 6
With an outer radius of 10 cm and inner radius of 6 cm, area = π(10² − 6²) = π × 64 ≈ 201.06 cm², the width is 4 cm, and the outer and inner circumferences are about 62.83 cm and 37.70 cm.
Frequently asked questions
What is an annulus?
An annulus is the ring-shaped region between two circles that share the same centre — think of a flat washer or a CD.
How do I find the area of a ring?
Subtract the inner circle's area from the outer circle's area: area = π(R² − r²).
Why must the inner radius be smaller?
The inner circle is the hole in the ring, so its radius must be less than the outer radius for the annulus to exist.
What units should I use?
Use the same length unit for both radii; the area is then in that unit squared (for example cm²).
What is the width of an annulus?
The width is the difference between the two radii, R − r — how thick the ring is.
Related calculators
Circle Area and Circumference Circle Area and Circumference is a mathematics calculator that helps you calculate the area of a geometric shape from its dimensions. The formula used is: Area = π×r²; Circumference = 2π×r; Diameter = 2r. Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units. Circle Sector Calculator Circle Sector Calculator is a mathematics calculator that helps you calculate circle properties such as area, perimeter, and radius. The formula used is: Arc length = r×θ; Area = r²θ/2; Chord = 2r·sin(θ/2); Perimeter = arc + 2r (where θ is in radians). Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units. Ellipse Calculator Ellipse Calculator is a mathematics calculator that helps you calculate ellipse values from your input data. The formula used is: Area = π×a×b; Perimeter ≈ π(a+b)[1 + 3h/(10+√(4−3h))] where h=(a−b)²/(a+b)²; e = √(1−(b/a)²); c = √(a²−b²). Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units.