Circular Sector Area Calculator
Enter the radius and central angle of a circular sector to find its area, arc length and chord. Switch between degrees and radians and the angle in radians is shown too.
How to find the area of a sector
- Enter the radius of the circle.
- Enter the central angle and choose degrees or radians.
- Read the area, arc length and chord length instantly.
Examples
Quarter circle, r = 5, angle = 90 degrees
radius = 5, angle = 90 deg
area = 19.635, arc length = 7.854, chord = 7.0711
Radius 2, angle = PI/3 radians
radius = 2, angle = 1.047198 rad
area = 2.0944, arc length = 2.0944, chord = 2
Frequently asked questions
What is the formula for the area of a sector?
The area equals one half times the radius squared times the central angle in radians. Degrees are converted to radians before the calculation.
How is the arc length found?
The arc length equals the radius times the central angle in radians. It is the curved edge of the sector, not the straight chord.
What is the chord of a sector?
The chord is the straight line joining the two end points of the arc. It equals two times the radius times the sine of half the angle.
Can I use degrees or radians?
Both. Pick the unit that matches your angle. The tool also reports the angle in radians so you can check the conversion.
Why must the angle be at most a full turn?
A sector is a slice of one circle, so its angle cannot exceed 360 degrees or two pi radians. Larger values are rejected.
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