Reading and Drawing Pie Charts

What you will learn

• Read a pie chart as parts of a whole.
• Find slice angles from frequencies.
• Find percentages and counts from angles.

Before you start: you should know that a full turn is $360^\circ$, how to work out fractions of an amount and what a percentage is. See Angles and Bar Charts.

The idea

A pie chart is a circle cut into slices. The whole circle stands for the total, and each slice stands for one category. A bigger slice means a bigger share. Pie charts are good for showing how a total splits into parts, but they do not show exact counts unless you label them.

Drawing a pie chart: from frequency to angle

1. Add up the frequencies to get the total.
2. Divide $360^\circ$ by the total to find the angle for one item.
3. Multiply each frequency by that angle.
4. Check that the angles add to $360^\circ$.

Reading a pie chart

A slice of $90^\circ$ is a quarter of the whole, which is $25\%$. To find how many people a slice stands for, find the fraction of the circle and take that fraction of the total.

Worked examples

Example 1: Drawing the angles

A survey of $60$ pupils: bus $18$, walk $24$, car $12$, cycle $6$. Find the angles.

1. $360 \div 60 = 6^\circ$ per pupil.
2. Bus $18 \times 6 = 108^\circ$, walk $24 \times 6 = 144^\circ$, car $12 \times 6 = 72^\circ$, cycle $6 \times 6 = 36^\circ$.
3. Check: $108 + 144 + 72 + 36 = 360$.

Answer: $108^\circ$, $144^\circ$, $72^\circ$, $36^\circ$

Example 2: From angle to people

A pie chart shows $200$ people. A slice has an angle of $72^\circ$. How many people?

1. $72 \div 360 = \tfrac{1}{5}$.
2. $\tfrac{1}{5}$ of $200 = 40$.

Answer: $40$ people

Example 3: Percentages

A slice has an angle of $54^\circ$. What percentage is it?

1. $54 \div 360 = 0.15$.
2. $0.15 \times 100 = 15\%$.

Answer: $15\%$

Tip: if the total divides $360$ neatly, such as $20$, $30$, $40$, $45$ or $60$, the angles are whole numbers. Otherwise use a calculator and round.

Why it matters

Pie charts appear in budgets, election results, market share reports and surveys. Knowing how to turn a total into slices helps you read them critically, for example by checking that the percentages really add up to $100\%$.

Practice

Your turn. Type or choose an answer, then press Check. Getting one wrong is fine, that is what practice is for. You can try as many times as you like.

Question 1 of 8

$40$ pupils were asked about favourite sports. $10$ chose swimming. What angle does swimming get, in degrees?

Your answer

Check

Question 2 of 8

$40$ pupils were asked. $6$ chose tennis. What angle does tennis get, in degrees?

Your answer

Check

Question 3 of 8

A slice of a pie chart has an angle of $90^\circ$. What percentage of the whole is it?

Your answer

Check

Question 4 of 8

$120$ people were surveyed. A slice has an angle of $30^\circ$. How many people is that?

Your answer

Check

Question 5 of 8

$60$ pupils were asked how they travel to school. $24$ walk. What angle do they get, in degrees?

Your answer

Check

Question 6 of 8

$45$ people were surveyed. How many degrees does each person get?

Your answer

Check

Question 7 of 8

All the slices of a pie chart add up to how many degrees?

Your answer

Check

Question 8 of 8

A slice is $25\%$ of a pie chart. The total is $80$ people. How many people is that?

Your answer

Check