Free Maths Calculator

Sector and Arc Calculator

Arc lengths and sector areas from the radius and the angle, treated as the same single idea: the angle over 360 tells you what fraction of the circle you own, and that fraction scales the full circumference or the full area. Answers come exact in pi and as decimals.

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    Worked Example

    A sector has radius 6 cm and angle 90°. Find the arc length and sector area.

    1. The fraction of the circle:90 ÷ 360 = 14
    2. Arc = 14 × 2π × 6 = 3π ≈ 9.425 cm
    3. Area = 14 × π × 36 = 9π ≈ 28.27 cm²

    Answer: Arc 3π cm, area 9π cm²

    Try These Yourself

    A semicircle has radius 10 cm. What is its arc length, in terms of π?Show answerHide answer

    Answer: 10π cm

    Half of 2π × 10.

    A sector of 60° has radius 9 cm. Sector area in terms of π?Show answerHide answer

    Answer: 13.5π cm²

    60360 is 16, and 81π ÷ 6 = 13.5π.

    What fraction of a circle is a 120° sector?Show answerHide answer

    Answer: 13

    120 ÷ 360.