Åk 6–9
3.2 The Circumference of a Circle
Have you ever considered how you measure the perimeter or more commonly called circumference of a circle?

One way you can do this it to roll a circle one rotation on a even surface and then measure the distance the circle has rolled.  One distance is equal to one rotation of the circle.

1 rotation = circumference

We can also see here that 3 diameters and a bit more is the circumference.
We can say that:

The circle’s circumference ≈ 3 · the diameter.

If we look for a relationship for 3 circles between their diameters and their circumferences, we get the following. The circumference values are rounded.

If we divide the circumference with the diameter, we get the same number, 3.14. This number is called pi. Pi is a number with an infinite number of decimals. The symbol for pi is p.

When approximating, we can use the nearest value of 3.
If you have to have a more exact answer, then we use the value of 3.14. On many calculators, there is a key for Pi, it gives a much better value.

So we can see that the relationship between the circumference, the diameter, and p (pi) is:

p = C ÷ d
C = d · p
C = 2r · p