How to Draw Pie Charts - GCSE Maths Help

What are pie charts?​

Pie charts are a popular way of displaying data and an excellent format for quickly showing the comparative sizes of the groups being recorded. A pie chart is a circle split into sectors, with each sector representing a different group. The size of each sector is proportional to the size of the group it represents.
In this article, we will look at how to convert each group in a data set into the correct angle and how to add these to a circle in order to complete the pie chart. Don't be anxious about maths. Let's dive in!

Pie chart example one: Favourite pets​

For our first example, thirty children in a class were each asked what their favourite pet is. The results are shown in the table below.

Pet	Frequency
Dog	16
Cat	6
Fish	3
Other	5

Converting the table into a pie chart

The first thing to do is double-check the total frequency. 16 + 6 + 3 + 5 = 30 which matches what we were told in the question. 16/30 people love dogs—that's a fraction. We now need to find the angle size for each group based on the fraction of a circle.
A pie chart is a circle, and we know that there are 360° in a circle. To split the circle equally between each of the thirty children in the survey, we therefore do 360 ÷ 30 = 12°. Each child must then be worth 12°. We can now find the sector size for each group by multiplying this 12° by the number of children in the group.

Pet	Frequency	Angle
Dog	16	16 × 12 = 192°
Cat	6	6 × 12 = 72°
Fish	3	3 × 12 = 36°
Other	5	5 × 12 = 60°

Checking angles and constructing the pie chart

An important step now is to add all of our angles together to confirm that they equal 360°.
192 + 72 + 36 + 60 = 360°
If at this point you answer does not equal 360° (allowing for rounding errors when dealing with decimals) double-check your working until it does total 360°.
We can now add the angles to the pie chart. Start with a circle and draw a starter line from the centre to the circumference. I like to make this line vertical up to the top, but it doesn't really matter.

Drawing a pie chart - step 1

We now measure the first angle round from our starter line. I've measured clockwise 192°, but direction doesn't matter.

Adding the 192 degree angle

We now measure the second angle round from the last line we drew, ensuring we continue in the same direction (in my case clockwise).

Adding the next angle to the pie chart

We now add the last two sectors. The last sector should just be the gap remaining when all the other sectors are done, but again it is important to check our working by measuring it to make sure it equals the 60° we are expecting.

Adding the final two sectors to the pie chart

Once all of the sectors have been added, it is time to colour in the pie chart using a different colour for each sector. We then add a key to the side of the pie chart to show what each colour represents. Alternatively the group headings can be written inside each sector on the chart.

Complete pie chart with key

There we have it, our completed pie chart. Anybody looking at this chart can see instantly that slightly over of half the class prefer dogs, while fish is the smallest group. This easy readability is a key positive for pie charts when compared to other types of graph or chart.

Practise drawing your own pie charts or read on for another example

To get some practice of drawing your own pie charts you can download some free pie chart worksheets complete with answers.
Alternatively, carry on reading for another example of how to construct a pie chart.

Pie chart example two: Colours of cars in a car park

Colour	Frequency
Red	21
Blue	13
Silver	26
White	8
Black	14
Other	6

By adding together the six numbers in the frequency column we find that there are 88 cars in the car park in total. We now find the angle size per car as before by dividing the 360 degrees of the circle by this total frequency.
360 ÷ 88 = 4.09°.
Therefore each car is worth 4.09° which we will then multiply by each individual frequency to get the separate sector sizes.

Colour	Frequency	Angle
Red	21	21 × 4.09 = 85.9°
Blue	13	13 × 4.09 = 53.2°
Silver	26	26 × 4.09 = 106.3°
White	8	8 × 4.09 = 32.7°
Black	14	14 × 4.09 = 57.3°
Other	6	6 × 4.09 = 24.5°
Totals	88	359.9°

Why do we have 359.9​°?

You can see at the bottom of the table that when the separate angles are added they come to a total of 359.9°. This is nothing to worry about. It is simply a problem to do with the rounding used when we divided 360 by 88. As 0.1° is such a tiny angle, this won't be a problem when we construct the pie chart, just err on the large side when estimating the decimal part of each angle measurement.

Constructing the pie chart

As before, we begin with a circle with one line drawn from the centre to the circumference. We then measure the first angle, 85.9°, round from this. The second angle, 53.2°, is measured from the end of the first sector and so on. Once we have drawn the first five sectors, there should be a gap of 24.5° remaining for the final sector. If not, check all of your measurements.

Above we have the completed sectors of the pie chart, with each angle matching up to the angles in the table.
The final step, as before, is to colour in each sector and add the key. In a situation like this, where the groups represent colours, it makes sense to colour each sector accordingly as seen below.

A pie chart showing the colours of cars in a car park

Summary: How to draw a pie chart

To convert data into a pie chart, complete the following steps:

1. Add up the separate group frequencies to find the total frequency.
2. Divide 360° by the total frequency to find the angle for each item.
3. Multiply your answer to step 2 by each group frequency to find the angle for each group's sector. Remember to check that these add back up to 360°.
4. Draw a circle with one line from the centre to the circumference and measure your first group's angle round from the line.
5. Continue measuring each sector from the end of the previous sector, ensuring that the last sector gets you back to your starting line.

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