The circumference of a circle worksheet. Using Pi and the diameter to find the perimeter.

The perimeter of a circle is known as the circumference of the circle (the distance around the circle). If you have the diameter of the circle (the distance across the centre) then the circumference (C) is found by the following formula:

C = πd

Alternatively, you can use the formula C = 2πr as the diameter is twice the radius. However, in the examples that follow, the first formula shall be used. Also, the symbol π represents Pi, which is a mathematical constant equal to 3.14 (to 2 decimal places). It’s best to use the Pi button on your scientific calculator in the examples that follow.

Example 1

Work out the circumference of a circle of diameter 5 yards.

So if you have remembered the formula above then all you need to do is multiply the diameter of 5 by Pi:

C = πd

= π × 5

= 15.7 yards to 1 decimal place

Example 2

The rim of a cup has a diameter of 2 inches. Work out the circumference of the cup to 1 decimal place.

So all you need to do is plug in the diameter of 2 inches into the above formula:

C = πd

= π × 2

= 6.3 inches to 1 decimal place

Example 3

A large circular window has a radius of 3.5 feet. Work out the circumference of the window to 1 decimal place.

This time the question gives you the radius of the circle. So you need to double this value to give the diameter:

2 × 3.5 = 7 feet.

So the diameter of the window is 7 feet which you can now plug into C = πd.

C = πd

= π × 7

= 22.0 feet to 1 decimal place.

Example 4

The circumference of a circle is 50m. Work out the diameter of the circle to 1 decimal place.

This time you are calculating the diameter from the circumference, so you will need to make the diameter the subject of the formula. Since Pi is multiplied by d, then divide both sides of the formula by Pi:

C = πd (divide by π)

C/ π = d

d = C/ π

Now that d is the subject of the formula, then all you need to do is substitute C = 50 into this formula:

d = 50/π

d = 15.9m to 1 decimal place.

So working out the circumference of a circle is actually quite easy to do as you just need to multiply the diameter by Pi. Make sure that you memorise the formula C = πd and don’t mix it up with other formulas involving Pi such as the area of a circle (A = πr²).