Calculators
Annulus Calculator
Calculate annulus area, ring width, inner and outer circumference, and total boundary length from two concentric radii.
Calculate the area and boundaries of a circular ring.
An annulus is the flat ring between two concentric circles. Enter outer radius R and inner radius r using the same unit, with R > r ≥ 0. Area = π(R − r)(R + r), ring width = R − r, outer circumference = 2πR, inner circumference = 2πr, and total boundary length = 2π(R + r). For R = 5 and r = 3, area is 16π ≈ 50.2654824574 square units, width is 2 units, and total boundary length is 16π units. An inner radius of zero gives a disk. Divide diameters by two before entering them. Positive radii must be from 1e-50 to 1e50. Results use browser floating-point arithmetic rounded to 12 significant digits; extremely close radii can round to the same number and will be rejected. This is a flat area calculator, not a torus volume calculator. All inputs stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What is the annulus area formula?
Area is π(R² − r²), evaluated as π(R − r)(R + r) to reduce cancellation. R is the outer radius and r is the inner radius.
Is total boundary length the outer circumference?
Total boundary length adds both circular boundaries: 2πR + 2πr. Outer circumference alone is 2πR.
Can the inner radius be zero?
Yes. Zero gives a full disk. The outer radius must be positive and strictly greater than the inner radius.
Should I enter radii or diameters?
Enter radii measured from the shared center. Divide each diameter by two and use the same unit for both inputs. Area uses squared units; width and boundaries use length units.
What inputs are supported?
Use zero for the inner radius or positive radii from 1e-50 to 1e50. Decimal and scientific notation are supported. Calculations stay in your browser and results are rounded to 12 significant digits.