Annulus Calculator
Ring area, outer circle, and width.
What it does
Washers, gaskets, and tree rings share one shape: a disk minus a disk. Area follows the difference of squares times pi, so small inner growth cuts less than matching outer growth adds. One outer and one inner radius fix area, edging, and width together.
The tool above runs the trio. With outer 10 cm and inner 6 cm, area is 201.06 cm2 with a 62.83 cm outer circle and 4 cm of width. With outer 8 cm and inner 5 cm, area is 122.52 cm2. The imperial mirror at 3.9 in over 2.4 in gives 29.69 in2 in the same proportions.
Zero inner means a full disk, while matched radii mean no ring at all. Validation enforces inner below outer so the root error of a negative ring never ships. Doubling both radii quadruples area while doubling width, which is why gasket pricing follows area rather than thickness.
This page assumes flat concentric circles. It does not do volume, eccentric bores, or oval flanges. For tubing weight, multiply area by length and density after.
How to use
- Pick metric (cm) or imperial (in).
- Enter the outer radius.
- Enter the inner radius below outer.
- Read ring area first.
- Read the outer circle for edging.
- Read width for gasket checks.
Formula
- R
- Outer radius in cm or in.
- r
- Inner radius in the same unit, below outer.
- width
- Straight radial thickness.
Flat ring with concentric circles. At zero inner radius the area is the full disk; at matched radii the area is zero. Units stay in one system per calculation.
Worked example
Example: ring 10 cm over 6 cm
Defaults: metric outer 10 cm with inner 6 cm. Imperial mirror is 3.9 in with 2.4 in.
- Inputs (metric default): outer 10 cm with inner 6 cm.
- Squares: 100 minus 36 is 64.
- Area: pi times 64 is 201.06 cm2.
- Outer: 2 pi times 10 is 62.83 cm.
- Width: 10 minus 6 is 4 cm. Tool shows the same.
Reference table
| Radii | Area | Outer |
|---|---|---|
| 10 over 6 cm | 201.06 cm2 | 62.83 cm |
| 8 over 5 cm | 122.52 cm2 | 50.27 cm |
| 5 over 3 cm | 50.27 cm2 | 31.42 cm |
| 3.9 over 2.4 in | 29.69 in2 | 24.5 in |
| 6 over 0 cm | 113.1 cm2 | 37.7 cm |
Limits
- Flat concentric only. Eccentric excluded.
- Area only. Volume needs length.
- No tolerances. Fit needs plus minus.
- Exact to floating point.
Common mistakes
- Using diameters as radii, quadrupling error.
- Subtracting radii before squaring.
- Mixing cm with inches.
- Allowing inner above outer.
- Reading circumference as area.
Try it yourself
Quick checks. Answers sit tucked under each question.
Outer 8 cm with inner 5 cm?
Area is pi times (64 minus 25) is 122.52 cm2. Outer is 50.27 cm with 3 cm width.
Outer 5 cm with inner 3 cm?
Area is pi times (25 minus 9) is 50.27 cm2. Outer is 31.42 cm with 2 cm width.
Questions
What is the ring formula?
Area = pi (R squared minus r squared). Here 201.06 cm2.
How is the outer circle figured?
2 pi R. Here 62.83 cm.
What is the ring width?
R minus r. Here 4 cm.
What happens with zero inner?
At zero inner the ring is a full disk pi R squared.
Can radii match?
No. Inner must sit below outer. Equal radii give no ring.
What happens if I double the size?
Area squares with radius. Double both and area quadruples.