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.

- What is Circumference?
- Parts of a Circle
- Circumference Formula
- How To Find Circumference
- Find Diameter From Circumference
- Find Radius From Circumference

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

**Circumference**-- The distance around the circle (the perimeter of a circle).**Diameter**-- The distance from the circle through the circle's center to the circle on the opposite side. (twice the radius)**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.

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.

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

$C=\pi d$

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

$C=2\pi r$

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

Here we have a circle with a given diameter of $\mathrm{12,756.274}kilometers$:

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

$C=\pi d$

$C=\pi \times \mathrm{12,756.274}km$

$C=\mathrm{40,075.016}km$

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 $2.75meters$. To find the circumference of the circle that is King Arthur's table, we use the radius formula:

$C=2\pi r$

$C=2\times \pi \times 2.75m$

$C=17.27m$

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.

That same equation, $C=\pi d$, 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 $339.292feet$. What is the diameter of the circle?

$C=\pi d$

$292feet=\pi d$

$\frac{292}{\pi}=\frac{\pi d}{\pi}$

$108feet=d$

No, that diameter is not random; it is the size of the sarsen stone ring at Stonehenge.

The circumference equation using radius, $C=2\pi r$, can also be used to find the radius of the circle if you know circumference.

Say we have a circle with a circumference of $40.526meters$; 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 $:

$C=2\pi r$

$526m=2\pi r$

$\frac{526m}{2\pi}=\frac{2\pi r}{2\pi}$

$45m=r$

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.

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.

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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