Pie charts are a popular way to display categorical data and appear frequently on Foundation and Higher GCSE Maths papers across AQA, Edexcel and OCR. You need to be able to calculate the angle for each sector, draw a pie chart using a protractor, and read information from existing pie charts. These are reliable marks if you follow the method carefully. This guide covers every skill with worked examples and practice questions. For an overview of every topic, see our complete GCSE Maths topics list.
What Is a Pie Chart?
A pie chart is a circular diagram divided into sectors. Each sector represents a category, and the angle of the sector is proportional to the frequency of that category. The total of all angles in a pie chart is 360 degrees.
Key Formulas
The first formula is used when drawing a pie chart; the second when reading one.
Step-by-Step Method
- Find the total frequency by adding all the frequencies.
- For each category, calculate the angle: (frequency ÷ total) × 360.
- Check your angles add up to 360 degrees.
- Draw a circle and mark a starting radius.
- Use a protractor to measure each angle from the previous line, drawing a new radius each time.
- Label each sector with the category name.
Worked Example 1 — Foundation Level
Question: A survey asks 60 pupils their favourite sport. Football: 24, Tennis: 12, Swimming: 15, Other: 9. Draw a pie chart.
Working:
Total = 60.
Football: (24 ÷ 60) × 360 = 144 degrees.
Tennis: (12 ÷ 60) × 360 = 72 degrees.
Swimming: (15 ÷ 60) × 360 = 90 degrees.
Other: (9 ÷ 60) × 360 = 54 degrees.
Check: 144 + 72 + 90 + 54 = 360 degrees.
Draw a circle, mark a start line, and use a protractor to measure each angle in turn. Label each sector.
Answer: Angles are Football 144, Tennis 72, Swimming 90, Other 54.
Worked Example 2 — Higher Level
Question: A pie chart shows the results of a survey of 180 people. The sector for "Agree" has an angle of 140 degrees. (a) How many people agreed? (b) The sector for "Disagree" represents 45 people. What angle does it have?
Working:
(a) Frequency = (140 ÷ 360) × 180 = 25200 ÷ 360 = 70 people.
(b) Angle = (45 ÷ 180) × 360 = 16200 ÷ 180 = 90 degrees.
Answer: (a) 70 people agreed. (b) The Disagree sector has an angle of 90 degrees.
Worked Example 3 — Exam Style
Question: Two pie charts compare how 40 boys and 50 girls travel to school. In the boys' chart, the "Bus" sector is 126 degrees. In the girls' chart, the "Bus" sector is 108 degrees. Who has more bus travellers?
Working:
Boys who take the bus: (126 ÷ 360) × 40 = 5040 ÷ 360 = 14 boys.
Girls who take the bus: (108 ÷ 360) × 50 = 5400 ÷ 360 = 15 girls.
Answer: 15 girls take the bus compared to 14 boys, so more girls travel by bus.
Common Mistakes
- Angles not adding to 360. Always check your calculated angles sum to 360 degrees before drawing.
- Inaccurate protractor use. Measure from the previous radius line, not from the starting line each time.
- Comparing pie charts without using frequencies. A larger sector in one pie chart does not necessarily mean a larger frequency if the totals are different — always convert to actual numbers.
- Rounding errors. If angles do not come out as whole numbers, round sensibly and adjust the last angle so the total is exactly 360.
Exam Tips
- Show all angle calculations clearly — this earns method marks even if your drawing is slightly inaccurate.
- If a question asks you to interpret two pie charts with different totals, you must calculate the actual frequencies before comparing.
- Use a sharp pencil and ruler for radii. Neat, accurate sectors earn full marks.
- For related data display, see reading and drawing bar charts. For key formulas, visit our GCSE Maths formulas page.
Practice Questions
Q1 (Foundation): A class of 30 pupils chose their favourite colour: Red 10, Blue 8, Green 7, Yellow 5. Calculate the angle for each colour.
Q2 (Foundation): A pie chart has a sector of 90 degrees for "Walking" out of a total of 200 people. How many people walk?
Q3 (Higher): Two pie charts show data for 80 adults and 120 children. The "Cinema" sector is 90 degrees for adults and 60 degrees for children. Which group has more cinema-goers?
Practise drawing and reading pie charts free on GCSEMathsAI.
Related Topics
Summary
- A pie chart displays categorical data as sectors of a circle, with angles proportional to frequency.
- To draw a pie chart, calculate each angle using (frequency ÷ total) × 360, then measure with a protractor.
- To read a pie chart, use (angle ÷ 360) × total to find the frequency for a sector.
- Always check your angles sum to 360 degrees before drawing.
- When comparing two pie charts with different totals, convert angles to actual frequencies before making comparisons.
Test your understanding
5 quick MCQs to identify any misconceptions on this topic.
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