Answer first
What this calculator tells you
Calculate the area, width and edge length of a ring from its outer and inner radius. Size a washer, a pipe wall, a running track or a garden path around a circle. Formula: Area = π × (R² − r²); ring width = R − r; combined edge length = 2π × (R + r). At the worked-example inputs, the ring area is 201.1. Holding every other input steady, moving outer radius from 8 to 12 moves the result from 88 to 339.3.
Transparent method
The formula
Size a washer, a pipe wall, a running track or a garden path around a circle.
Worked example
Example inputs
How to interpret the result
A ring's area is the big disc minus the hole, and the difference grows faster than the ring is wide. An outer radius of 10 with an inner radius of 6 leaves a ring 4 wide with an area of about 201 square units. A 4 wide ring near the center of a small disc would hold far less. That is why a washer, a pipe wall and a running track all need the two radii, not just the width.
At the worked-example inputs the ring area is 201.1. It rises with outer radius and falls as inner radius increases.
Formulas assume ideal geometric shapes. Real-world measurements carry their own error, and every input must use the same unit: mixing feet and inches silently produces a wrong answer.
Before you rely on it
What to check
Measure both radii from the same center. If you have diameters, halve them first, and make sure the inner value is the smaller one.
The common error
Where people go wrong with annulus area calculator
Multiplying the ring width by the circumference of the outer circle. That ignores the curve of the ring and overstates the area, more so as the ring gets wider.
Sensitivity evidence
How outer radius changes the ring area
Holding every other input at the worked-example value, moving outer radius from 8 to 12 moves the ring area from 88 to 339.3: a spread of 251.3, or 125% of the worked-example result.
| Outer radius | Ring area | Ring width | Combined edge length |
|---|---|---|---|
| 8 | 88 | 2 | 88 |
| 9 | 141.4 | 3 | 94.2 |
| 10worked example | 201.1 | 4 | 100.5 |
| 11 | 267 | 5 | 106.8 |
| 12 | 339.3 | 6 | 113.1 |
Every input, tested
Which input moves the ring area most
Of the 2 inputs, outer radius moves the ring area most (125.7 across the range tested) and inner radius moves it least (45.2).
| Input | Tested from | To | Ring area at each end | Swing |
|---|---|---|---|---|
| Outer radius | 9 | 11 | 141.4 to 267 | 125.7 (63%) |
| Inner radius | 5.4 | 6.6 | 222.6 to 177.3 | 45.2 (23%) |
Two variables at once
Ring area by outer radius and inner radius
Across the grid the ring area runs from 38.2 to 380. Moving outer radius from 8 to 12 shifts it by 251.3 at the middle column, and moving inner radius from 4.8 to 7.2 shifts it by 90.5 at the middle row, so outer radius is the bigger lever here.
| Outer radius \ Inner radius | 4.8 | 6 | 7.2 |
|---|---|---|---|
| 8 | 128.7 | 88 | 38.2 |
| 9 | 182.1 | 141.4 | 91.6 |
| 10 | 241.8 | 201.1 | 151.3 |
| 11 | 307.8 | 267 | 217.3 |
| 12 | 380 | 339.3 | 289.5 |
The highlighted cell is the worked example: 201.1.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Outer radius | 10 | Enter the outer radius used in this calculation. |
| Inner radius | 6 | Enter the inner radius used in this calculation. |
| Ring area | 201.1 | |
| Ring width | 4 | |
| Combined edge length | 100.5 | |
Inputs, definitions and assumptions
Outer radius
Enter the outer radius used in this calculation. The prefilled worked-example value is 10.
Inner radius
Enter the inner radius used in this calculation. The prefilled worked-example value is 6.
How to use this calculator
- 1Verify the inputs. Gather outer radius and inner radius from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the ring area at 201.1. Store your own version of it as Scenario A.
- 3Test one change. Start with outer radius, the input with the biggest effect here: moving outer radius from 9 to 11 takes the ring area from 141.4 to 267, a swing of 63% of the worked-example figure.
- 4Check the boundary. Read the interpretation boundary above before acting on the result.
People also ask
Frequently asked questions
How do you calculate annulus area?
Area = π × (R² − r²); ring width = R − r; combined edge length = 2π × (R + r). At the worked-example inputs the ring area is 201.1.
What does the annulus area result mean?
Size a washer, a pipe wall, a running track or a garden path around a circle. At the worked-example inputs the ring area is 201.1. It rises with outer radius and falls as inner radius increases.
How much does outer radius change the ring area?
Holding every other input at the worked-example value, moving outer radius from 8 to 12 moves the ring area from 88 to 339.3, a spread of 251.3.
What are the limits of this annulus area calculator?
Formulas assume ideal geometric shapes. Real-world measurements carry their own error, and every input must use the same unit: mixing feet and inches silently produces a wrong answer. The tables on this page test outer radius only from 8 to 12; a value outside that range is not tabulated here.
Which input moves the ring area most in the annulus area calculator?
Ranked by how far each moves the ring area across the range tested: outer radius (125.7, 63%) and inner radius (45.2, 23%).
How much does inner radius matter in the annulus area calculator?
The worked example uses 6. With the other inputs left at the worked example, moving inner radius from 5.4 to 6.6 takes the ring area from 222.6 to 177.3, a swing of 23% of the worked-example figure.
Which inputs change the ring width in the annulus area calculator?
At the worked-example inputs it is 4. Outer radius takes it from 3 to 5 and inner radius takes it from 4.6 to 3.4.
Which inputs change the combined edge length in the annulus area calculator?
At the worked-example inputs it is 100.5. Outer radius takes it from 94.2 to 106.8 and inner radius takes it from 96.8 to 104.3.
Why is a trapezoid's height not its slanted side?
Area needs the perpendicular distance between the two parallel sides. The slanted side is longer, so using it overstates the area. Measure straight across, at right angles to the bases.
Sources and evidence
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