Math Tip of the Day: Circle Arc Length

When it comes to math and circles, the list of concepts goes on and on.  One concept of circles is arc length.  An arc is section of the circumference of a circle.  And the arc length is the length of that section.  To calculate the arc length, you can set up a proportion (see diagram and example below).

circle arc length

The ration of the arc length and the circumference is proportional to the ratio of the central angle measure and the total degrees of the circle.  Keep in mind that the arc is part of the circumference, and the central angle measure is a part of the total degrees.  So that makes it all proportional.

Back to the example.  First, substitute the values for C and r (C= central angle measure, r = radius).  Then multiply the values in the denominator of the first ratio.  Cross multiply and divide, and you have your answer!

Check back next week for more tips on circles.