Pie charts, explained with examples
A pie chart shows how a whole is split into parts, with each sector's angle proportional to its share. Drawing and reading pie charts both come down to one number: how many degrees represent one item.
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The key idea
A full circle is 360°, and it represents the whole data set. So each item gets an equal share of the 360°:
degrees per item = 360 ÷ total frequency
Multiply each frequency by this number to get its angle. Equivalently, angle = (frequency ÷ total) × 360°. The angles must add up to 360°, which is a useful check.
Drawing a pie chart
- Find the total frequency.
- Work out 360 ÷ total.
- Multiply each frequency by that value to find each angle, and check they add to 360°.
- Draw a circle and a radius from the centre to the edge as a starting line.
- Use a protractor to measure each angle from the previous line, drawing each sector in turn.
- Label each sector or add a key.
Example 1: calculating angles
40 students recorded how they travel to school: walk 18, bus 12, car 6, cycle 4. Find the angles for a pie chart.
- 360 ÷ 40 = 9° per student.
- Walk: 18 × 9 = 162°. Bus: 108°. Car: 54°. Cycle: 36°.
- Check: 162 + 108 + 54 + 36 = 360°. This is the pie chart above.
Example 2: an awkward total
A survey of 72 people chose their favourite fruit: apples 30, bananas 24, grapes 18. Find the angles.
- 360 ÷ 72 = 5° per person.
- Apples 150°, bananas 120°, grapes 90°.
Example 3: a total that does not divide neatly
Of 35 people, 12 chose red. Find the angle for red, to the nearest degree.
- (12/35) × 360 = 123.4…
- 123°. When rounding, check the angles still add to 360°, adjusting the largest slightly if necessary.
Reading a pie chart
To find a frequency from a pie chart, reverse the process: frequency = angle ÷ degrees per item. If you know the total, degrees per item is 360 ÷ total. If you know one sector's frequency and angle, you can find degrees per item from that sector.
Example 4: finding frequencies
A pie chart shows how 180 people voted. The sector for Option A has an angle of 140°. How many voted for A?
- Degrees per person: 360 ÷ 180 = 2°.
- Votes for A = 140 ÷ 2 = 70.
Example 5: from one known sector
In a pie chart, the 'cats' sector is 80° and represents 20 people. The 'dogs' sector is 128°. How many people chose dogs, and how many were surveyed?
- 80° = 20 people, so 1 person = 4°.
- Dogs: 128 ÷ 4 = 32 people.
- Total surveyed = 360 ÷ 4 = 90 people. If a frequency comes out as a fraction, recheck your angle reading.
Example 6: percentages
A sector has an angle of 90°. What percentage of the data does it represent?
- 90/360 = 1/4.
- 25%.
Pie charts on the non-calculator paper
Exam totals are usually chosen so that 360 divides neatly, such as 20, 24, 30, 36, 40, 45, 60, 72, 90 or 120. If you get an awkward value, check the total first. A useful shortcut is to simplify the fraction: for 15 out of 60, 15/60 = 1/4, and a quarter of 360° is 90°. Recognising halves (180°), quarters (90°), thirds (120°) and sixths (60°) saves time on both drawing and reading questions.
Pie charts and other topics
Pie chart questions often link to ratio, fractions and percentages. If the angles for two categories are 120° and 80°, the ratio of their frequencies is 120 : 80 = 3 : 2, because the angles are in the same proportion as the frequencies. Similarly, the fraction of the whole for any sector is its angle over 360. Seeing these links lets you answer questions without finding every frequency.
Comparing two pie charts
This is a classic trap. Two pie charts can only be compared by proportion, not by number, unless you know both totals. If 60% of School A walks and 40% of School B walks, you cannot say more School A students walk: School B might be much larger. A correct comparison says “a greater proportion of School A students walk”. To compare actual numbers, use each chart's total to work out the frequencies.
Example 7: comparing correctly
In a pie chart of 120 Year 10 students, 'football' is 90°. In a pie chart of 300 Year 11 students, 'football' is 60°. Which year has more students choosing football?
- Year 10: 90/360 × 120 = 30 students. Year 11: 60/360 × 300 = 50 students.
- Year 11 has more students choosing football, even though its sector is smaller. Year 10 has a greater proportion.
When to use a pie chart
Pie charts work well for showing how a single whole is divided into a small number of categories, such as how a budget is spent. They are less good when there are many small categories, when values are very close, or when you need to compare exact amounts, where a bar chart is usually clearer. Pie charts are for categorical data; for continuous data such as heights, use a histogram or a frequency polygon instead, because they show how values are spread.
Common mistakes
- Using 100 instead of 360 as the total angle.
- Measuring each angle from the starting line instead of from the previous sector.
- Comparing numbers between two pie charts with different totals.
- Rounding angles so they no longer add up to 360°.
Practice questions
Try each one before opening the answer.
Q1. 60 people are surveyed. How many degrees represent one person?
Show answer
Q2. In a survey of 90, a category has 25 people. Find its angle.
Show answer
Q3. A sector of 45° represents 15 people. How many were surveyed?
Show answer
Q4. A sector is 30% of a pie chart. Find its angle.
Show answer
Frequently asked questions
Are pie charts on the Foundation paper?
Yes. Drawing and interpreting pie charts are on both tiers, often with a protractor question on the calculator or non-calculator paper.
How accurate does my drawing need to be?
Mark schemes usually allow about ±2° for each angle. Use a sharp pencil and line the protractor up carefully on each new starting line.
Key takeaways
- Degrees per item = 360 ÷ total.
- Angle = frequency × degrees per item; angles add to 360°.
- Frequency = angle ÷ degrees per item.
- Compare pie charts by proportion unless you know both totals.
- Pie charts suit a small number of categories in one whole.