Circumference of a Circle

A circle is a shape with all points the same distance from the center. It is named by the center. The circle to the left is called circle A since the center is at point A. If you measure the distance around a circle and divide it by the distance across the circle through the center, you will always come close to a particular value, depending upon the accuracy of your measurement. This value is approximately 3.14159265358979323846... We use the Greek letter  (pronounced Pi) to represent this value. The number  goes on forever. However, using computers,  has been calculated to over 1 trillion digits past the decimal point.

The distance around a circle is called the circumference. The distance across a circle through the center is called the diameter.  is the ratio of the circumference of a circle to the diameter. Thus, for any circle, if you divide the circumference by the diameter, you get a value close to . This relationship is expressed in the following formula:
where  is circumference and  is diameter. You can test this formula at home with a round dinner plate. If you measure the circumference and the diameter of the plate and then divide  by , your quotient should come close to . Another way to write this formula is:  where · means multiply. This second formula is commonly used in problems where the diameter is given and the circumference is not known (see the examples below).

The radius of a circle is the distance from the center of a circle to any point on the circle. If you place two radii end-to-end in a circle, you would have the same length as one diameter. Thus, the diameter of a circle is twice as long as the radius. This relationship is expressed in the following formula: , where  is the diameter and  is the radius.