Circumference of a circle

The circumference of a circle is the distance around the circle. It is another name for the perimeter of a circle.

Circle with diameter and circumference labelled

The circumference of a circle is calculated using the formula: \text{circumference} = \pi \times \text{diameter}

Pi (π)

For any circle:

\text{circumference} \div \text{diameter} = 3.1415 \dotsc

This number is Pi. It is a number which goes on forever.

\pi = 3.1415926535897932384626433832795 \dotsc

The pi symbol ( \pi) allows you to give the exact value to a calculation involving circles as pi cannot be written as an exact fraction or decimal. If a decimal answer is required, the value can be approximated as 3.14 (3 significant figures).

Scientific calculators have a \pi button which can be used during calculations, with the final answer being rounded off as appropriate.

Example

Calculate the circumference of the dartboard.

Dartboard

The diameter is twice the radius.

d = 20 \times 2 = 40~\text{cm}

Circumference = 40 \times \pi = 125.7~\text{cm} (1 decimal place).

The answer can also be given in terms of \pi. In this case the answer is 40 \pi~\text{cm}.

The circumference formula can be used to solve problems.

Question

How many full rotations will the wheel make if it travels 3,500 cm?

Car tyre of radius, 27.5cm

Circumference of the wheel is: 27.5 \times 2 \times \pi = 172.8~\text{cm} (1 decimal place)

In one rotation the wheel travels 172.8 cm (or 55 \pi).

To calculate the number of rotations:

3,500 \div 172.8 = 20.25 (or 3500 ÷ 55\pi = 20.26

This is 20 full rotations.

curriculum-key-fact
In this case, rounding off early did not change the final answer. For the most accurate answer you should avoid rounding off until the end if possible.