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Arc Length

The length of an arc is the measure of the distance along the curved line.

Since the arc length of a complete circle with radius r is equal to the circumference, or 2π r , the length l of a smaller arc can be found using the formula

where C is the central angle of the arc in degrees .

Take for example the arc below, in which C = 108 and r = 5.

Math diagram

Then

If the central angle is measured in radians , the formula is simpler:

 

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