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Circular Arc Length and Sector Area — result sheet
Arc length and sector area from a radius and central angle in degrees or radians.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: θ in radians; arc s = rθ; sector A = ½r²θ.
Degrees convert to radians, then the radius scales them: arc length grows linearly with angle while sector area grows with the square of the radius.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Radius — minimum 1.0E-6; maximum 1000000000
- Central angle — minimum 0; maximum 1000000000
- Angle unit — 2 choices
Worked example
| Input | Value |
|---|---|
| Radius | 5 |
| Central angle | 60 |
| Angle unit | degrees |
Arc length 5.236; sector area 13.09.
Assumptions and limits
- Radius positive; angle zero or positive in the stated unit.
- Flat circle; arc and sector share the same central angle.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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