What are the 2 methods for working out the circumference of a circle?

The two ways to work out the circumference of a circle are C = 2πr or C = πd. The reason that these formulas are the same is because the diameter is double the radius, so if you replace d with 2r in C = πd you get the formula C = 2πr.

Example 1

Work out the circumference of this circle. Use both formulas C = 2πr and C = πd.

In this circle the radius of the circle is given as 8m (since you have the distance halfway across the centre).

First use C = 2πr.

Since you have the radius already then this can be plugged directly into C = 2πr:

C = 2 × π × 8

C = 50.3m to 1 decimal place.

Let’s see if you get the same answer with C = πd. With this formula you need the diameter of the circle (the distance all the way across) so double the radius (2 × 8 = 16). Now plug in d = 16 into the formula:

C = πd

C = π × 16

C = 50.3m to 1 decimal place.

As you can see both formulas give the same answer for the circumference of the circle.

Example 2

A circular shaped table has a diameter of 5 foot. Work out the circumference of the table using C = 2πr and C = πd.

First use C = 2πr. This formula uses the radius so you need to halve the diameter of the circle (5 ÷ 2 = 2.5m). Now plug in the radius of 2.5 into the formula:

C = 2 × π × 2.5

C = 15.7 foot to the nearest tenth.

Let’s compare this with C = πd. Just plug in d = 5 into this formula:

C = π × d

= π × 5

= 15.7 foot to the nearest tenth.

Like example 1, both formulas give the same answer for perimeter of the circular table.

So to summarise both methods C = 2πr and C = πd give exactly the same answers.