Circumference

The circumference of a circle is the distance around the circle.

Circumference formula

The ratio of the circumference to the diameter of any circle is a constant known as pi (π), which is equal to approximately 3.14159. From this relationship, we can derive the formula for the circumference of a circle:

C = πd

where C is the circumference and d is the diameter of the circle.


Using radius instead of diameter, the formula is:

C = 2πr

where r is the radius of the circle.


If the area of a circle is given, the circumference can be found using the formula:

where A is the area of the circle.

Examples:

1. What is the circumference of a circle with radius 4.4?

Since we are given the radius, we can use C = 2πr to get

C = 2π(4.4) = 8.8π ≈ 27.646


2. A circle has an area of 100π. What is the circle’s circumference?

Using the formula ,

Circumference of an ellipse

A circle is a special case of an ellipse where the minor and major axes (a and b in the figure below) are equal. To find the circumference of an ellipse, use the following formula:

where C is the circumference, and a and b are the lengths of the semi-axes of the ellipse. This equation is just an estimation because a more exact formula requires the use of non-elementary functions.

If we were to plug in equal values for a and b, say r, we would get the equation for the circumference of a circle:

C =
=
= 2πr