How to find the arc length of a circle.

Hi Welcome to MooMooMath. Today we are going to look at how to find arc length. Now arc length gets confused with arc measure so let me first define what arc length of a circle is. This central angle of a circle is 60 degrees so this arc measure is 60 degrees. We have 360 degrees in a circle so the arc is the same as the central angle as far as the measure. Now we are looking for arc length. Arc length is a fraction of the circumference. So the circumference is 24 inches, we would have a fraction of that in this proportion. So that is what we are looking at. The first thing we need to do is to know the measure of the arc. So we know the measure of the arc is 60 degrees because the central angle is 60 degrees then we will take that and plug it into our formula. Since this is a fraction of the circumference d pi is in our formula and d is our diameter our radius is 9 so our diameter would add up to 18 inches. So I will plug 18 into our diameter times pi and that will equal the circumference of my circle. Now this arc is not the whole circle, so what fraction of the circle is it? I take 60 out of 360 because 60 is my arc measure and that is one sixth of my circle so I will multiple the circumferences which is 18 pi by my fraction one sixth. When I multiply that together I get 18 over 6 times pi which is three pi. So there you go. That is how you find the arc length of a circle. Since the whole circumference is 18 pi I will take one sixth of it, which is three pi. Here are the rules of arc length. Remember arc length is a part of or a fraction of the circumference. To find the arc length take the measure of the arc over 360 (reduce that) times the circumference (you can replace the circumference with diameter times pi. Take the fraction times d pi and that is arc length. Hope this was helpful.