Pie Charts

Learn how to read pie charts and calculate the angles and percentages that each sector represents.

What Is a Pie Chart?

A pie chart is a circle divided into sectors (slices) where each sector represents a category of data. The size of each slice shows what proportion of the total that category makes up.

The full circle = $360°$ = $100\%$ of the data.

Note

Pie charts are best for showing how a total is split into parts. You see them in news articles, sports statistics, and science reports.

Reading a Pie Chart

To find the percentage of a sector, use:

$\text{Percentage} = \frac{\text{angle of sector}}{360} \times 100$

Example: A pie chart shows favourite fruits. The "Apple" sector has an angle of $90°$ . What percentage chose apple?

$\frac{90}{360} \times 100 = \frac{1}{4} \times 100 = \mathbf{25\%}$

To find the actual number from the percentage, multiply by the total:

$\text{Frequency} = \frac{\text{angle}}{360} \times \text{total}$

If 120 students were surveyed: $\frac{90}{360} \times 120 = 30$ students chose apple.

Drawing a Pie Chart

To draw a pie chart, first find the angle for each category:

$\text{Angle} = \frac{\text{frequency}}{\text{total}} \times 360$

Example: 20 students were asked their favourite colour.

Colour	Frequency	Angle
Blue	8	$\frac{8}{20} \times 360 = 144°$
Red	5	$\frac{5}{20} \times 360 = 90°$
Green	4	$\frac{4}{20} \times 360 = 72°$
Other	3	$\frac{3}{20} \times 360 = 54°$
Total	20	360°

Tip

Always check that your angles add up to exactly $360°$ . If they don't, you've made a calculation error somewhere.

Comparing Sectors

When two sectors are given, you can compare them directly:

Example: In a pie chart of 60 students, "Football" = $150°$ and "Tennis" = $90°$ .

Football: $\frac{150}{360} \times 60 = 25$ students
Tennis: $\frac{90}{360} \times 60 = 15$ students

Football is more popular by $25 - 15 = 10$ students.

Warning

You cannot compare two pie charts directly just by looking at the sizes of slices — the totals may be different! Always calculate the actual numbers first.

Real world: household budget breakdown

A family's monthly income of €3000 is spent as follows: rent €1200, food €600, transport €300, savings €450, other €450. Converting to angles: rent $= \frac{1200}{3000} \times 360 = 144°$ . A pie chart makes the budget instantly visual — rent dominates at nearly half the circle.

Real world: sports injury statistics

A sports-medicine study of 240 athletes recorded injury type: muscle strain 96, joint sprain 72, fracture 48, other 24. Muscle strain angle $= \frac{96}{240} \times 360 = 144°$ . The pie chart helps coaches identify which injury type requires the most prevention effort.

Tip Before drawing a pie chart, verify that all your angles add up to exactly 360°. Round each angle to the nearest degree and adjust the largest category to make up any rounding difference.

Practice Problems

A pie chart has a sector with an angle of $72°$ out of a total of 50 students. How many students does this sector represent?

Show answer

$\dfrac{72}{360} \times 50 = 0.2 \times 50 = 10$ students.

30 students chose their transport to school. 12 walked. What angle represents 'walking' on a pie chart?

Show answer

$\dfrac{12}{30} \times 360 = 0.4 \times 360 = 144°$.