Annulus (Ring) Area Calculator
Find the area, width, and inner and outer circumferences of an annulus (a flat ring) from its outer and inner radii.
units
units
Area between the two circles
64%
of outer diskRing area
64%
Inner hole
36%
- 1
Outer disk area
π × 10² = 314.1593Area of the full outer circle. - 2
Inner disk area
π × 6² = 113.0973 - 3
Ring area
314.1593 − 113.0973 = 201.06
How does this calculator work?
An annulus is the ring between two concentric circles. Its area equals π(R² − r²), where R is the outer radius and r the inner radius. The ring width is R − r, the outer circumference is 2πR, and the inner circumference is 2πr. Enter both radii (with R > r) to compute all four.
Formula
How this is calculated
An annulus is the flat ring-shaped region between two concentric circles. You supply the outer radius R and the inner radius r, where R must be greater than r and both are measured from the shared center in the same length unit.
The ring area is the area of the large disk minus the area of the small disk: π·R² − π·r², which factors to π(R² − r²). The radial width of the ring is simply R − r, and the boundary lengths are the standard circle circumferences 2πR for the outer edge and 2πr for the inner edge. Area comes out in square units; width and circumferences in linear units.
The result is only valid when R > r ≥ 0. If r equals 0 the annulus becomes a full disk, and if r equals R the area collapses to zero. The donut chart shows the ring area as a fraction of the full outer disk πR², visualizing how much of the disk the hole removes.
Frequently asked questions
An annulus is the region bounded by two concentric circles — a flat ring, like a washer or a CD. Its area is the difference between the outer and inner disk areas.
The inner circle has to fit inside the outer one for a ring to exist. If r ≥ R the area would be zero or negative, so the calculator requires R > r ≥ 0.
The area is in square units of whatever length unit you enter (e.g., cm gives cm²), while the width and circumferences are in those same linear units.
Also known as
TG we-Calculate Editorial Team. (2026). Annulus (Ring) Area Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/annulus-calculator
TG we-Calculate Editorial Team. "Annulus (Ring) Area Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/annulus-calculator.
TG we-Calculate Editorial Team, "Annulus (Ring) Area Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/annulus-calculator
@misc{wecalculate_annulus_calculator, title = {Annulus (Ring) Area Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/annulus-calculator}}, year = {2026}, note = {TG we-Calculate} }
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