When to use this calculator
Subtract the isosceles triangle from the circular sector to get the segment between the chord and arc.
Explore the circle & ellipse calculators for other questions in this topic. For a related calculation, use the Circular Sector Perimeter Calculator: Find the boundary length of a sector bounded by an arc and two radii.
PUTTING IT INTO PRACTICE
Circle Segment 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 | 2 |
| Central angle (degrees) | 180 |
| Result | 6.283185 square units |
- Check the input labels and enter the example values above.
- Apply the relationship: Segment area = r²(θ − sin θ)/2, with θ in radians.
- The result is 6.283185 square units, rounded for display.
How to interpret your result
This tool covers the minor segment with a central angle no greater than 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 circle segment area calculator useful?
Subtract the isosceles triangle from the circular sector to get the segment between the chord and arc.
How do I use the circle segment 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?
Segment area = r²(θ − sin θ)/2, with θ in radians.
What should I check before using the result?
This tool covers the minor segment with a central angle no greater than 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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