ClarityHow to use this tool
- Enter the circle radius in metres, not its diameter.
- Enter the central angle in degrees, measured at the centre of the circle.
- Calculate the straight-line chord. Use arc length if you need the curved distance along the circumference.
Input reference and sample values
Use the units and choices shown for each field. Sample values are provided for practice, not as recommendations.
| Input | Format and units | Sample |
|---|---|---|
| Radius | Numeric value. Unit: m. Must be greater than zero. | 3 |
| Central angle | Numeric value. Unit: degrees. Zero or positive. Maximum: 360. | 60 |
Result for these sample inputs
3 m
Select Try the example in the form to load these values and calculate them again. This replaces the current form inputs. Compare the result with the method and worked explanation below.
The method, explained
Chord = 2r × sin(angle/2), with degrees converted to radians.
With radius 3 m and central angle 60°, chord = 2 × 3 × sin(30°) = 3 m. At 180°, the chord becomes the diameter, 6 m.
Understanding your result
A chord is the straight segment between two points on the circumference. Its length cannot exceed twice the radius. Angles θ and 360° − θ give the same chord because they describe the same endpoints from opposite directions around the circle.
What to keep in mind
Assumes an ideal circle, a positive radius and a central angle from 0° to 360°. At 0° or 360° the endpoints coincide. This is not the arc length or a radius measured from a drawing scale.
Common questions
Is chord length the same as arc length?
No. A chord is straight; the arc follows the circle. For a nonzero minor angle, the curved distance is longer.
What if I know the diameter?
Divide it by two before entering the radius. For a 6 m diameter, enter 3 m.
Methodology maintained by ClarityKit. How these tools are built and checked.