Central Angle from Arc Length
Find a circle’s central angle and chord from a measured arc length.
Your numbers
Central angle
Use consistent units. The result follows the assumptions you enter.
Scenario comparison
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Formula
Use θ = s/r and c = 2r sin(θ/2). s is arc length and r is radius in the same unit. θ is radians before conversion to displayed degrees; c is chord length.
Find a circle’s central angle and chord from a measured arc length.
Worked example
- Radius (m)
- 3
- Arc length (m)
- 3.141592653589793
- Central angle
- 60 °
- Chord length
- 3 m
Scope and limitations
Use consistent units. The result follows the assumptions you enter.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.
Formula version: b97076892448 · Example checked: