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.


1

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

2

Circumference of a Circle Formula

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


3

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 Calculation

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

1

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

2

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 Radius Calculation

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

Circle Radius Calculation

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∏.