When to use this calculator
A chord is straight, while an arc follows the circumference. Their lengths only become close for small angles.
Explore the circle & ellipse calculators for other questions in this topic. For a related calculation, use the Circle Area Calculator: Calculate the area enclosed by a circle from its radius.
PUTTING IT INTO PRACTICE
Chord Length: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Radius | 5 |
| Central angle (degrees) | 60 |
| Result | 5 units |
- Check the input labels and enter the example values above.
- Apply the relationship: Chord = 2r sin(angle/2).
- The result is 5 units, rounded for display.
How to interpret your result
Uses the minor central angle between 0° and 180°.
Distinguish radius from diameter before entering measurements. Arc length follows the curve, while chord length runs straight between endpoints. Ring-shaped areas subtract the inner circle from the outer one.
Frequently asked questions
How is chord length different from arc length?
A chord is a straight line between two points on the circle. An arc follows the circular boundary between those points.
When is the chord length calculator useful?
A chord is straight, while an arc follows the circumference. Their lengths only become close for small angles.
How do I use the chord length calculator?
Enter radius, central angle (degrees). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Chord = 2r sin(angle/2).
What should I check before using the result?
Uses the minor central angle between 0° and 180°.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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