Perimeter and Circumference

Hello. My name is Vickie Vickery and I have been a Middle and High School Math teacher for 14 years. Today's lesson will be useful to students taking Math in the 7th and 8th grade. On the following pages students will learn how to find the perimeter of polygons and the circumference of circles.


In our lesson, we want to find the distance around a circle. But we do not call it perimeter but circumference. A circle is not a polygon, but a closed curve in the plane which begins and ends at the same point. Every point on the closed curve is the same distance from the a fixed point within.  Measuring the circumference of a circle, however is more difficult than measuring the perimeter of a polygon. It is easy to measure the diameter of a circle which is the line segment that goes through the center of a circle with both endpoints on the circle. It has been proven that the circumference of a circle is about 3 1/7 times the diameter of the circle. This fact can be shown by measuring the diameter of a circle with a string and carefully place the string on the circle. Now see how many times does the length of the diameter go around the circle. As you may have found, it takes three diameters with a little bit left over no matter how large or small the circle.

This relationship is so important that it is represented by the Greek letter p [pie] spelled pi. The fraction 3 1/7 and the decimal 3.14 are the most often used approximations of p; however, a more exact, but still approximate value of p is 3.14159. Pi is an irrational number, and therefore has a nonterminating, nonrepeating decimal representation.

If we multiply the diameter d by p, we can find the circumference of the circle. Therefore we use the formula C = pd where C = circumference, p = 3.14 or 3 1/7, and d = diameter.

Since it takes two radii to make a diameter, we can substitute 2r, where r = radius, for the d (diameter) in the formula to make a new formula when the radius is given:  C = 2rp or as it is usually written C = 2pr.

Remember always to record the unit of measure with your answer for the perimeter and circumference.

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The views expressed on this page are not necessarily those of the University of South Carolina. (March, 2000)