When to use this calculator
Find the boundary length of a sector bounded by an arc and two radii. Includes two radial edges even in limiting 0° or 360° inputs; for a whole-circle boundary use circumference.
Explore the circle & ellipse calculators for other questions in this topic. For a related calculation, use the Ellipse Area Calculator: Calculate the enclosed area of an ellipse using its two semi-axes.
PUTTING IT INTO PRACTICE
Circular Sector Perimeter: 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 | 17.853982 units |
- Check the input labels and enter the example values above.
- Apply the relationship: Sector boundary length = two radii + arc length.
- The result is 17.853982 units, rounded for display.
How to interpret your result
Includes two radial edges even in limiting 0° or 360° inputs; for a whole-circle boundary use circumference.
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 circular sector perimeter calculator useful?
Find the boundary length of a sector bounded by an arc and two radii. Includes two radial edges even in limiting 0° or 360° inputs; for a whole-circle boundary use circumference.
How do I use the circular sector perimeter 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?
Sector boundary length = two radii + arc length.
What should I check before using the result?
Includes two radial edges even in limiting 0° or 360° inputs; for a whole-circle boundary use circumference.
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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