When to use this calculator
Find the length of a circular arc from radius and central angle. Enter the angle in degrees, not radians.
Explore the circle & ellipse calculators for other questions in this topic. For a related calculation, use the Chord Length Calculator: Find the straight chord connecting two points on a circle.
PUTTING IT INTO PRACTICE
Arc 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) | 90 |
| Result | 7.853982 units |
- Check the input labels and enter the example values above.
- Apply the relationship: Arc length = 2πr × angle ÷ 360.
- The result is 7.853982 units, rounded for display.
How to interpret your result
Enter the angle in degrees, not radians.
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.
How do I use the arc 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?
Arc length = 2πr × angle ÷ 360.
What should I check before using the result?
Enter the angle in degrees, not radians.
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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