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A sector is the "pie slice" portion of a circle, while a segment is the region cut off by a straight chord — related but distinct areas that both depend on the radius and central angle.
This calculator finds the sector area, arc length, and segment area from the radius and central angle.
How it works
Enter the radius and central angle in degrees. The calculator finds the sector area and arc length as a proportion of the full circle, then subtracts the triangular portion (formed by the two radii and the chord) to find the segment area.
- Enter radius.
- Enter central angle (degrees).
- Click Calculate to see your results.
Examples
Radius 10, angle 90°
A quarter-circle sector (90°) with radius 10 has a sector area of about 78.54, an arc length of about 15.71, and a segment area of about 28.54.
Who should use it
- Checking geometry coursework involving circle sectors and segments.
- Calculating material needed for a pie-slice or curved-segment shaped design.
Industry applications
- Geometry education
- Engineering and design (curved component calculations)
Advantages
- Calculates sector area, arc length, and segment area together from one input.
- Uses exact trigonometric formulas, not approximations.
Limitations
- Requires the angle in degrees — convert first if you have it in radians.
Common mistakes to avoid
- Confusing sector area with segment area — they're only the same when the central angle is very small.
- Entering the angle in radians instead of degrees.
Best practices
- Use sector area for "pie slice" style problems and segment area specifically when a straight chord (not two radii) bounds the region of interest.
Tips
- For a semicircle (180°), the segment area equals exactly half the circle's area, since the "triangle" being subtracted degenerates to a straight line with zero area.