Calculate the area, perimeter, and arc lengths of an annulus sector quickly and easily.
Perimeter (P)
Arc Lengths (outer / inner)
Area (A)
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Step 01
Input the outer radius (R), the inner radius (r), and the angle (α).
Step 02
Ensure both radii are in the exact same unit of measurement (e.g., cm or inches).
Step 03
The outer radius must always be greater than the inner radius (R > r), otherwise the ring doesn't exist.
Step 04
The calculator instantly determines the area, perimeter, and both arc lengths.
| Value | Formula |
|---|---|
| Area (A) | A = (α/360°) · π · (R² - r²) |
| Outer Arc (b_R) | b_R = 2 · π · R · (α/360°) |
| Inner Arc (b_r) | b_r = 2 · π · r · (α/360°) |
| Perimeter (P) | P = b_R + b_r + 2(R - r) |
The outer radius R must always be larger than the inner radius r. The ring width is derived from R - r.
Enter the angle in degrees (maximum 360°). An angle of 360° corresponds to a full circular ring (annulus).
If R and r are entered in cm, the area is automatically calculated in cm² and the perimeter in cm.
An annulus sector (or circular ring sector) is a portion of an annulus bounded by two radii (or a central angle). It looks like a curved piece of ribbon or a slice of pie with the tip cut off.
The area is calculated by subtracting the area of the inner circular sector from the outer one: A = (α / 360°) · π · (R² - r²). Where R is the outer radius, r is the inner radius, and α is the angle.
Calculate the area, outer/inner circumference, and width of a circular ring (annulus) online with step-by-step formulas.
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To calculatorAn annulus sector (often referred to as a circular ring sector) is a 2D geometric shape created by extracting a "slice" from a full circular ring. Mathematically, it is defined by three specific variables: the outer radius, the inner radius, and the central angle that bounds the sector.
This tool is not only helpful for geometry homework but is heavily utilized in material planning for construction (e.g., curved masonry) or mechanical engineering (flange segments). To compute the area of annulus sector formula, you essentially subtract the area of the smaller inner circular sector from the larger outer sector. For more fundamental mathematical definitions regarding circular segments, you can read the Wikipedia page on the Annulus.
Liability Disclaimer: All calculations provided on this website serve as an orienting guide and are without guarantee. For exact static, architectural, or safety-critical engineering, always verify the results with professional CAD software.