How to Find Arc Length

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Arc length

An arc is any portion of the circumference of a circle. Arc length is the distance from one point to another. Arc length is the distance from one endpoint to the arc of the other. It requires knowing a bit about the geometry of a circle.  Here is a step by step guide on how to find arc length. 

How to find arc length using a measurement of Central angle in Degrees

  1. Set up the formula for arc length. Arc length = 2π(r)(Θ/360)
    where r equals the radius of the circle and Θ equals the measurement of the arc’s central angle, in degrees.

  2. Plug the given length of the circle’s radius into the formula.
    For example, if the circle’s radius is 20 cm, your formula will look like this:  Arc length = 2π(20)(Θ/360)

  3. Insert the given value of the arc’s central angle into the formula.
    For example, if the arc’s central angle is 145 degrees, your formula will look like this: Arc length = 2π(20)(145/360)

  4. Multiply the radius by 2π. For example 2π(20)(145/360)
    2(3.14)(20)(145/360)
    (125.6)(145/360)

  5. Divide the arc’s central angle by 360. For example (125.6)(145/360)
    (125.6) (0.402)

  6. Multiply the two numbers together. For example (125.6) (0.402)
    50.49

How to find arc length using a measurement of Central angle in Radians

  1. Set up the formula for arc length. The formula is arc length = Θ(r), where Θ equals the measurement of the arc’s central angle in radians, and r equals the length of the circle’s radius.

  2. Plug the length of the circle’s radius into the formula. For example, if the circle’s radius is 20 cm arc length = Θ(20).

  3. Insert the measurement of the arc’s central angle into the formula. For example, if the arc’s central angle is 3.72 radians,
    (3.72) (20).

  4. Multiply the radius by the radian measurement. (3.72) (20) = 74.4