Annulus area
Annulus area A = π(R² − r²): enter the outer and inner radius to get the ring area plus the inner and outer areas, circumferences and the ring width; an inner radius that is not smaller than the outer one is rejected, as is any non-positive value.
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Result
One quantity per line, ready to copy.
Enter an outer radius to calculate
What this tool does
- Compute the area of a washer, flange, pipe wall section or ring paving, and get the inner and outer circumferences for sealing or cutting.
- Compare how width and area change across inner/outer radius pairs to pick a specification.
- Verify the formulas: ring area π(R² − r²) and width R − r.
Example
Input
3
Output
外半径 3 内半径 1 的圆环面积：25.132741 外圆面积 πR²：28.274334 内圆面积 πr²：3.141593 外圆周长 2πR：18.849556 内圆周长 2πr：6.283185 环宽 R − r：2 长度单位 u，面积 u²，体积 u³
With an outer radius of 2 and an inner radius of 1 the ring area is 3π ≈ 9.424778, the outer circle 4π ≈ 12.566371, the inner π ≈ 3.141593 and the width 1 — all canonical.
Frequently asked questions
What if the two radii are equal?
It reports an error. The width and area would both be 0, a degenerate case; the inner radius must be strictly smaller than the outer one so you never get a meaningless zero.
Why not use π(R+r)(R−r)?
The two forms are algebraically identical (difference of squares); the tool uses R² − r² because it reads more directly. Both lose precision when the radii are very close — use symbolic maths if you need more.
What is the ring width?
Width = R − r, the radial thickness of the ring, which maps directly onto the wall thickness in a washer or pipe specification.
Keywords：圆环面积annulus area垫圈内外圆几何计算环宽