DIY Cost Tools
Annulus Area Calculator
Calculate ring area, radial width, and both circumferences from concentric circle radii. Enter dimensions in one consistent unit for an immediate estimate.
Outer radius must be positive and greater than the nonnegative inner radius. Use the same length unit throughout. Maximum input: 1 trillion.
How to use
Measure radius from the center to the edge, rather than across the entire circle. Convert measurements to a common unit, enter them above, and select Calculate. Default results appear on page load. Areas use squared input units; volumes use cubed input units. Results are rounded to ten significant digits.
Formula and explanation
A = π(R − r)(R + r); width = R − r; outer perimeter = 2πR; inner perimeter = 2πr. R is the outer radius and r is the inner radius. The factored area formula reduces cancellation for close radii.
Worked example
Outer radius 5 and inner radius 3 produce area 16π ≈ 50.2655 square units and width 2 units.
Important limitations
Assumes perfect concentric circles in a flat plane. Radial width does not describe an off-center hole. Material orders may need waste and joint allowances. This does not evaluate structural strength. Measurement uncertainty and floating-point precision can affect results.
Frequently asked questions
Can I enter diameters?
Divide both diameters by two first.
What if the inner radius is zero?
The area is a full circle and the inner circumference is zero.
Is width the difference between diameters?
No. Radial width is half that difference.
Which units can I use?
Any length unit, provided both inputs use the same unit.
Review notes
Reviewed October 1, 2026. Default outputs were independently checked against geometric formulas. Required fields, invalid dimensions, excessive values, and geometric boundary cases were tested. Educational and planning estimates only.