Turn frequencies into sector angles to draw a pie chart, and read frequencies back from a pie chart's angles. It is a Foundation topic, aimed at grade 2. Free questions with answers are on this page. Worked examples show each line before you try the questions.
A pie chart is a whole of 360∘ split in proportion to frequency. Each person (or item) is worth 360÷total degrees. For 20 people, one person is 18∘, so 5 people would be 90∘. The other way: a 90∘ sector of 60 people is a quarter of the class, so 15 people.
To draw one, work out each angle, check they sum to 360∘, then measure from a radius with a protractor. Label each sector with the category (and the frequency or percentage if it helps).
Pie charts compare parts of one whole. They are a poor way to compare two different totals — a bar chart is clearer then. At this grade you mostly need the angle ↔ frequency conversion.
Objectives
The angle is the fraction of the total, times 360°.
Divide the angle by 360 to get the fraction, then multiply by the total.
The angles must add to 360°.
Key points
Work out the angle for one item: 360∘÷ total frequency.
Work out each sector angle and check they add up to 360∘.
Draw sectors accurately with a protractor and label them.
Find a frequency from a sector angle when the total is known.
Worked examples
Example 1
A pie chart shows the drinks chosen by 36 people. 3 of them chose tea. What is the angle for tea?
2 marks
The full circle is 360° for 36 people, so each person is worth 360 ÷ 36 = 10°.
3 people × 10° = 30°.
The angle for tea is 30°.
Answer: 30°
Common slips
Slip: The full circle is 362° for 36 people, so each person is worth 360 ÷ 36 = 10°. That changes a number from the question, so it answers a different question.
Slip: 6 people × 10° = 30°. That changes a number in the working, so the step no longer follows from the one before.
Slip: The angle for tea is 34°. That does not match the working above it.
Example 2
A pie chart shows 36 people. The angle for bus is 30°. How many people chose bus?
2 marks
Each person is worth 360 ÷ 36 = 10°.
Number of people: 30 ÷ 10 = 3.
3 people chose bus.
Answer: 3
Common slips
Slip: Each person is worth 362 ÷ 36 = 10°. That changes a number from the question, so it answers a different question.
Slip: Number of people: 33 ÷ 10 = 3. That changes a number in the working, so the step no longer follows from the one before.
Slip: 7 people chose bus. That does not match the working above it.
Example 3
Three slices of a pie chart have angles 100°, 90° and 50°. The rest of the pie is one more slice. What is its angle?
2 marks
The angles in a pie chart add to 360°. The three known angles add to 100 + 90 + 50 = 240.
360 − 240 = 120.
The last slice is 120°.
Answer: 120°
Common slips
Slip: The angles in a pie chart add to 362°. The three known angles add to 100 + 90 + 50 = 240. That changes a number from the question, so it answers a different question.
Slip: 360 + 240 = 600. That uses addition, but this step needs subtraction.
Slip: The last slice is 124°. That does not match the working above it.
Questions and answers
GCSE Maths pie charts questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
A pie chart shows the drinks chosen by 40 people. 6 of them chose tea. What is the angle for tea?
Show answer
Answer: 54°
The full circle is 360° for 40 people, so each person is worth 360 ÷ 40 = 9°.
6 people × 9° = 54°.
M1 — The full circle is 360° for 40 people, so each person is worth 360 ÷ 40 = 9°.
A1 — Answer 54°
Question 2 Easy2 marks
A pie chart shows 40 people. The angle for bus is 54°. How many people chose bus?
Show answer
Answer: 6
Each person is worth 360 ÷ 40 = 9°.
Number of people: 54 ÷ 9 = 6.
M1 — Each person is worth 360 ÷ 40 = 9°.
A1 — Answer 6
Question 3 Medium2 marks
A pie chart shows 30 people. The angle for bus is 24°. How many people chose bus?
Show answer
Answer: 2
Each person is worth 360 ÷ 30 = 12°.
Number of people: 24 ÷ 12 = 2.
M1 — Each person is worth 360 ÷ 30 = 12°.
A1 — Answer 2
Question 4 Medium2 marks
Three slices of a pie chart have angles 120°, 110° and 70°. The rest of the pie is one more slice. What is its angle?
Show answer
Answer: 60°
The angles in a pie chart add to 360°. The three known angles add to 120 + 110 + 70 = 300.
360 − 300 = 60.
M1 — The angles in a pie chart add to 360°. The three known angles add to 120 + 110 + 70 = 300.
A1 — Answer 60°
Question 5 Hard2 marks
Three slices of a pie chart have angles 130°, 120° and 50°. The rest of the pie is one more slice. What is its angle?
Show answer
Answer: 60°
The angles in a pie chart add to 360°. The three known angles add to 130 + 120 + 50 = 300.
360 − 300 = 60.
M1 — The angles in a pie chart add to 360°. The three known angles add to 130 + 120 + 50 = 300.
A1 — Answer 60°
Question 6 Hard2 marks
A pie chart shows the drinks chosen by 60 people. 6 of them chose tea. What is the angle for tea?
Show answer
Answer: 36°
The full circle is 360° for 60 people, so each person is worth 360 ÷ 60 = 6°.
6 people × 6° = 36°.
M1 — The full circle is 360° for 60 people, so each person is worth 360 ÷ 60 = 6°.
A1 — Answer 36°
Question 7 Exam-style2 marks
Three slices of a pie chart have angles 100°, 100° and 70°. The rest of the pie is one more slice. What is its angle?
Show answer
Answer: 90°
The angles in a pie chart add to 360°. The three known angles add to 100 + 100 + 70 = 270.
360 − 270 = 90.
The last slice is 90°.
M1 — The angles in a pie chart add to 360°. The three known angles add to 100 + 100 + 70 = 270.
A1 — Answer 90°
Common mistakes
Most lost marks on this topic are one slip.
Multiplying the fraction by 100 instead of 360.
The circle is 360°.
Using one category as the total.
The denominator is the total of every category.
Drawing a slice whose angle does not match the fraction.
Calculate the angle before you use the protractor.
Spot the slip
How many degrees are in a full circle?
360
180
100
Show the slip
360 A full turn is 360°.
Exam tips
This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Show the angle-per-item calculation (360÷30=12) and a table of angles — that is where the method marks are.
Draw angles to within 2∘ with a sharp pencil and protractor, and label each sector (not just a key) where possible.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.