What is Circumference?

Circumference is the distance around a circle. We can find the circumference using either the diameter or radius of a circle.

Circumference Of A Circle Definition

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.

Table Of Contents

  1. What is Circumference?
  2. Parts of a Circle
  3. Circumference Formula
  4. How To Find Circumference
  5. Find Diameter From Circumference
  6. Find Radius From Circumference

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, π. Pi is a mathematical constant and it is also the ratio of the circumference of a circle to the diameter.

Circumference Formula

Diameter To Circumference

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

C = πd

Radius To Circumference Formula

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

C = 2πr

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 12,756.274 kilometers:

To find its circumference, multiply that measurement times π:

C = πd

C = π × 12,756.274 km

C = 40,075.016 km

We did not select the diameter randomly. To three decimal places, that circumference of the earth's equator.

Circumference Example Earth's Diameter

The Encyclopedia Britannica tells us that a historic Round Table, rumored to be King Arthur's, has a radius of 2.75 meters. To find the circumference of the circle that is King Arthur's table, we use the radius formula:

C = 2πr

C = 2 × π × 2.75 m

C = 17.27 m

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, C = πd, can also be used to find the diameter of a circle if you know circumference. Just divide both sides by the irrational number π.

Suppose you are told the circle's circumference is 339.292 feet. What is the diameter of the circle?

C = πd

292 feet = πd

292π = πdπ

108 feet = d

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

Circumference To Diameter

Find Radius From Circumference

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

Say we have a circle with a circumference of 40.526 meters; what is its radius? We will again divide both sides by π, but we also need to eliminate the 2, so divide both sides by 2π:

C = 2πr

526 m = 2πr

526 m2π = 2πr2π

45 m = 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.

Next Lesson:

Circumference of Earth

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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Ashburn, VA

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