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Central Angle from Arc Length — result sheet
Calculate a circle's central angle and sector area from radius and arc length.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Central angle θ = arc length/radius in radians; degrees = θ×180/π; sector area = 1/2×radius×arc length.
Arc length first determines the angle in radians, and the same radius-arc pair determines the corresponding circular-sector area.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Radius — length; minimum 1.0E-6; maximum 1000000
- Arc length — length; minimum 0; maximum 10000000
Worked example
| Input | Value |
|---|---|
| Radius | 10 |
| Arc length | 5 |
Angle ≈ 28.648°; sector area = 25 square units.
Assumptions and limits
- Radius is positive and arc length is nonnegative in the same length unit.
- The arc is the minor or major arc represented by the nonnegative ratio; no orientation is inferred.
- A sector boundary and radius are ideal Euclidean geometry.
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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