 ## What is Circumference?

Circumference is the distance around a circle. We can find the circumference using either the diameter or radius of a circle. For shapes made of straight lines, we say they have a perimeter. For circles, the perimeter gets the name circumference.

It does not matter if the circle is a slice of a sphere (like earth's equator) or flat like King Arthur's gathering place for all his knights if we know either the diameter or the radius, we can find the circumference of a circle. I bet King Arthur would have welcomed Sir Cumference to his Round Table.

## Parts of a Circle

A circle (the set of all points equidistant from a given point) has many parts, but this lesson will focus on three:

1. Circumference -- The distance around the circle (the perimeter of a circle).
2. Diameter -- The distance from the circle through the circle's center to the circle on the opposite side. (twice the radius)
3. Radius -- The distance from the center of a circle to the circle (half the diameter). Draw a line segment from the center of the circle to any part of the circle and you have the radius.

## Circumference Formula

Two formulas are used to find circumference, $C$, depending on the given information. Both circumference formulas use the irrational number Pi, which is symbolized with the Greek letter, $\pi$. Pi is a mathematical constant and it is also the ratio of the circumference of a circle to the diameter. ### Diameter To Circumference

If you are given the circle's diameter, $d$, then use this circumference of a circle formula:

If you are given the radius, r, you can still find the circumference. If you know the radius, the circumference formula is:

You can always find the circumference of a circle as long as you know the diameter or the radius.

## How To Find Circumference

Here we have a circle with a given diameter of :

To find its circumference, multiply that measurement times $\pi$:

We did not select the diameter randomly. To three decimal places, that circumference of the earth's equator. The Encyclopedia Britannica tells us that a historic Round Table, rumored to be King Arthur's, has a radius of . To find the circumference of the circle that is King Arthur's table, we use the radius formula:

That is a massive table. Arthur supposedly gathered $25$ knights, though, so with all $26$ men gathered around, each had only $69$ centimeters of table edge to himself. They would have been elbow to elbow, those knights.

You can also find circumference with the area of a circle.

## Find Diameter From Circumference

That same equation, , can also be used to find the diameter of a circle if you know circumference. Just divide both sides by the irrational number $\pi$.

Suppose you are told the circle's circumference is . What is the diameter of the circle?

No, that diameter is not random; it is the size of the sarsen stone ring at Stonehenge. The circumference equation using radius, , can also be used to find the radius of the circle if you know circumference.

Say we have a circle with a circumference of ; what is its radius? We will again divide both sides by $\pi$, but we also need to eliminate the $2$, so divide both sides by $2\pi$:

Of course, that is not a random number. That is the size of Notre Dame Cathedral's famed South Rose Window. That is a huge big stained glass window!

This lesson has provided you with lots of information the circumference of circles and a way to find any the measure of any one part if you have another measurement. Along the way, you also learned a little geography and history, which may also come in handy to you.

### Next Lesson: Instructor: Malcolm M.
Malcolm has a Master's Degree in education and holds four teaching certificates. He has been a public school teacher for 27 years, including 15 years as a mathematics teacher.
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