Geometry · interactive lab
Arc length & sectors
Change a central angle to explore the corresponding arc, chord, and sector area.
Arc length & sectorsLIVE EXPLORATION
Change a value to see the connection
Your measurements
These formulas use θ in radians. The tool converts the entered degrees automatically. Angles above 180° describe major sectors.
Why it works
Arc length = rθ · Sector area = ½r²θ
A little question. A clearer picture.
Arc length & sectors: common questions
Wondering about the why? Start here.
How do I calculate arc length and sector area?
With θ in radians, arc length is rθ and sector area is r²θ/2. This tool accepts degrees and converts them automatically. For a 90° sector with radius 4, the arc length is 2π and the sector area is 4π.
Work through arcs and sectorsWhat is the difference between a chord and an arc?
A chord is the straight segment joining two points on a circle. An arc follows the curved circumference between them. For a central angle θ, the chord length is 2r sin(θ/2); the selected arc length is rθ when θ is in radians.
Explore circle measurements