Circle Sector Area Calculator
Angle unit
Try an example
Sector
The sector is 25% of the full circle (area 314.15927).
More measurements
- Chord length
- 14.142136
- Sector perimeter (arc + 2r)
- 35.707963
- Segment area (arc to chord)
- 28.539816
- Angle
- 90° = 1.5707963 rad
In degrees the same formulas read A = (θ/360)·πr² and s = (θ/360)·2πr. Units are whatever the radius uses: cm gives cm and cm².
Find the area and arc length of a circle sector from its radius and central angle in degrees or radians, along with the chord length, the sector's perimeter and the area of the segment between the arc and the chord.
Formula
Worked Example
90° is a quarter of the full circle, so the sector is a quarter of π × 10² = 314.16. The segment is the sector minus the right triangle formed by the two radii: 78.54 − 50 = 28.54.
Frequently Asked Questions
What is the formula for the area of a sector in degrees?
A = (θ/360) × πr². A 120° sector of a circle with radius 6 is a third of the circle: π × 36 ÷ 3 = 37.70.
What is the difference between a sector and a segment?
A sector is the slice bounded by two radii and the arc, like a slice of pizza. A segment is the region between the arc and the straight chord joining its ends; its area is the sector area minus the triangle ½r² sin θ.
How do I convert degrees to radians?
Multiply by π/180: 90° = π/2 ≈ 1.5708 rad, and 1 rad ≈ 57.30°. In radians the sector formulas are at their simplest: area ½r²θ and arc length rθ.