Annulus Area Calculator
The area of a ring or washer — the outer circle minus the hole in the middle.
An annulus is the region between two concentric circles, so the area is simply π(R² − r²) — the big disc minus the small one.
How the annulus area calculator works
An annulus is the region between two concentric circles, so the area is simply π(R² − r²) — the big disc minus the small one. It is the shape of a washer, a pipe wall in cross-section and a running track lane, and the same subtraction gives the material in a tube.
Formula: square a²; rectangle ab; triangle ½bh; circle πr²; parallelogram bh; trapezoid ½(a+b)h; ellipse πab
Worked examples
| Inputs | Area | Note |
|---|---|---|
| Outer 10, inner 6 | 201.0619 | 201.06 |
| A washer, 12 mm outer and 6 mm inner | 339.292 | 339.29 mm² |
| A thin ring | 311.0177 | 311.02 |
FAQFrequently asked questions
What is an annulus?
The ring between two circles that share a centre — the shape of a washer.
What is the formula?
π(R² − r²), the outer disc minus the inner one.
How do I find the area of a pipe wall?
Use the outer and inner radii here; multiply by the length for the volume of material.
Does it work if the circles are not concentric?
No — this formula assumes a common centre. An offset hole needs different geometry.
How thick is the ring?
The outer radius minus the inner one.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.