When to use this calculator
Calculate a circular sector’s area from radius and angle in degrees. A 360-degree sector is a whole circle.
Explore the circle & ellipse calculators for other questions in this topic. For a related calculation, use the Angle Between Vectors Calculator: Find the unsigned angle between two nonzero 3D vectors.
PUTTING IT INTO PRACTICE
Sector Area: 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 | 19.634954 square units |
- Check the input labels and enter the example values above.
- Apply the relationship: Area = πr² × angle ÷ 360.
- The result is 19.634954 square units, rounded for display.
How to interpret your result
A 360-degree sector is a whole circle.
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 sector area 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?
Area = πr² × angle ÷ 360.
What should I check before using the result?
A 360-degree sector is a whole circle.
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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