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 sectors
    What 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