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# What Is the Circumference of a Circle? Learn how and why the equation for the circumference of a circle works. Plus -- how is this formula used in the Olympic Games?

By
Jason Marshall, PhD
Episode #116

## How to Calculate the Circumference of a Circle

Now that we have a circle to work with, let’s investigate its circumference—aka, the distance around the outside of the circle. We could start this investigation by laying a long piece of string all the way around our 3-inch radius circle, cutting it so that the string is the same length as the circle’s circumference, and then laying this string out in a line and measuring its length with a ruler.

I certainly encourage you to carry out that little investigation if you want to, but the beauty of math is that we really don’t need to. Why? Because of the way that the number pi is defined. As we’ve talked about before, the number π = 3.14… is defined as the ratio of the circumference of a circle to its diameter. In other words, π = C / d. Which means that to find the circumference of any circle, we just have to juggle this equation around and find that C = π x d. And since we know that the diameter of a circle is just twice its radius, we can also find the circumference of a circle in terms of its radius—as known by school kids around the world: C = 2 x π x r. So to find the circumference of our 3-inch radius circle, all we really have to do is use this formula to get that C = 2 x 3.14… x 3 inches or about 18.84 inches.

## How Long Are the Olympic Rings?

So we now know how to calculate the circumference of a circle. But so what? Why is that important? Well, there are lots of reasons that you might want to make this calculation. For example, what if you wanted to use colored yarn to put together a giant tapestry of the 5 interlocking Olympic rings for your bedroom wall? If you were so inclined, all you’d need to know to find out how much yarn you’d need is the radius of your desired rings. If you want 1 foot radius rings, you need C = 2 x 3.14… x 1 foot or about 6.28 feet of string for each ring. Obviously this isn’t something most of us are ever going to want to do, which might leave you wondering if there are any real world applications of our famous formula?

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