Formula and example
How it is calculated
A=πr², C=2πr. For θ in radians: sector area=r²θ/2, arc length=rθ, chord=2r·sin(θ/2).
Worked example
With r = 3 cm and an angle of 90°, the quarter-circle area is 9π/4 ≈ 7.0686 cm². Its arc length is 3π/2 ≈ 4.7124 cm.
Things to check
- The segment lies between the chord and the selected arc. Angles above 180° produce the larger segment.
- An angle of 360° gives the full circle; the chord then has length 0.
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 its arc.