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How to use
A circular sector is the part of a disk bounded by two radii and their arc. From radius and central angle you can calculate sector area, arc length, chord length and the corresponding circular-segment area.
- Enter the radius and choose a length unit.
- Enter the angle and choose degrees or radians.
- Review sector area, arc, chord, sector perimeter and segment area.
How it is calculated
Example
For radius 10 and angle 90°: arc length = 5π ≈ 15.708 and sector area = 25π ≈ 78.540.
Important notes
The compact formulas s=rθ and A=½r²θ require radians; degree input is converted automatically. At 360°, the sector boundary is the circle circumference because the two radial sides coincide.
Worked examples and interpreting results
A sector of angle 90 degrees and radius 4 cm is a quarter circle. Its arc length is 2π cm and area 4π cm². Convert the angle to π/2 radians before applying radian formulas.
| Case | Calculation | Result |
|---|---|---|
| Arc length | 4 × π/2 | 6.283185 cm |
| Sector area | 0.5 × 4² × π/2 | 12.566371 cm² |
How to check the result
Arc length is not the full sector perimeter, which adds two radii. A sector is bounded by two radii and an arc; it differs from a circular segment bounded by a chord and an arc.
Frequently asked questions
What is the difference between a sector and a segment?
A sector is bounded by two radii and an arc; a segment is bounded by a chord and the arc.
Is chord length the same as arc length?
No. The chord is straight while the arc is curved.
Should the angle be entered in degrees or radians?
Use the unit selected in the calculator. The formula A=½r²θ requires radians; with degrees use A=(θ/360)πr². Mixing the two units produces an incorrect result.