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Results
Enter your dimensions above and the results appear here.
About the Sector & Arc Calculator
The sector & arc calculator is a free online tool: arc length, sector area, chord and segment. Enter radius (r) and central angle (θ) and the results update instantly, alongside a labelled diagram so you always know which measurement goes where.
Choose your input unit (mm, cm, m, km, in, ft or yd) and optionally show the results in a different one: lengths, areas and volumes are converted correctly. Every answer shows the formula behind it, and the calculation runs in your browser, so nothing is uploaded.
Sector & Arc Calculator example
Radius (r) = 6 cm
Central angle (θ) = 75°Sector area = 23.5619 cm²
Arc length = 7.854 cm
Chord length = 7.3051 cm
Sector perimeter = 19.854 cm
Segment area = 6.1753 cm²
Share of full circle = 20.8333 %How to use the Sector & Arc Calculator
- Pick the unit your measurements use. All dimensions must share the same unit.
- Enter radius (r) and central angle (θ). Focus a field to highlight the matching label on the diagram.
- Read the results as you type. The largest card is the main answer; the others are the related measurements.
- Copy a single value, copy everything, or share a link that keeps your inputs.
Sector & Arc Calculator FAQ
What formulas does the sector & arc calculator use?
s = rθ (θ in radians); A = ½r²θ; c = 2r·sin(θ/2); Segment = ½r²(θ − sin θ).
What is the difference between a sector and a segment?
A sector is the pie-slice between two radii and an arc. A segment is the region between a chord and its arc. This calculator gives both areas.
Can I use different units?
Yes. Pick the input unit and, if you like, a different output unit. Area results are shown in squared units and volumes in cubed units.
Is this sector & arc calculator free and private?
Yes. It is free with no sign-up, and calculations happen on your device, so your numbers are never sent to a server.
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