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Circle Chord Length — result sheet
Find the straight chord length determined by a circle radius and a minor central angle measured in degrees.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: c = 2r sin(theta/2), where theta is the central angle converted from degrees to radians.
A chord is the straight segment joining two points on a circle. The calculator converts the entered minor central angle to radians and evaluates twice the radius times the sine of half that angle.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Circle radius — length units; Positive circle radius in the length unit you are using.; minimum 1.0E-6; maximum 1000000
- Minor central angle — degrees; Included central angle from 0 through 180 degrees.; minimum 0; maximum 180
Worked example
| Input | Value |
|---|---|
| Circle radius | 5 |
| Minor central angle | 60 |
A radius of 5 and a 60-degree central angle give c = 2 x 5 x sin(30 degrees) = 5 length units.
Assumptions and limits
- The radius is positive and both endpoints lie on the same circle.
- The entered angle is the minor central angle from 0 through 180 degrees.
- The radius and chord share the same length unit; no unit conversion is performed.
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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