How to Calculate the Perimeter of a Circle

The perimeter of a circle is most commonly referred to as the circumference of a circle and we will use the word circumference for our explanation below.

Diameter of a Circle

Look at this diagram, here you can see the diameter – the distance from one side of the circle to the other side.

circle-diameter

Circumference of a Circle Formula

Now to calculate the circumference of the circle we multiply pi (∏) by the diameter (d) of the circle.

circle-circumference-formula

∏ is a fixed value equal to 3.14, or to be exact 3.1415926535897932384 but = 3.14 will do for our calculations.

Calculating the circumference using diameter.

We now know what the diameter is and the formula to use so now let’s calculate the circumference.

circle-circumference-calculation3

And there you have your answer, the circumference of a 10cm diameter circle is 31.4cm. If you want to be really exact you could leave your answer as 10∏.

 

Using the Radius to calculate the Circumference

Radius

An alternative method for calculating the circumference is by using the radius of the circle. The radius of a circle is the distance from the center to the edge of the circle. The radius equals half the diameter.

circle-radius

Calculating the circumference using the radius.

If we have the radius of a circle then to calculate the circumference we multiply pi (∏) by the radius (r) of a circle and then multiply by 2.

circle-circumference-radius-calculation

For the circle above we have a radius (r) of 5cm, so lets calculate the circumference:

circle-circumference-radius-calculation2

And again we have the same answer, the circumference of a 5cm radius circle is 31.4cm. Again, if you want to be really exact you could leave your answer as 10∏.