A pie chart has 4 equal sections. What fraction does each section represent?
Total is 1 whole.
4 equal parts → each is 1/4.
Pie Charts
Pie charts represent data as parts of a whole using sectors. Angles and percentages are used to show proportions visually.
Overview
A pie chart shows how a whole amount is split into parts.
The whole circle represents 360°, and each sector shows a proportion of the total.
Whole circle = \(360^\circ\)
Bigger sectors represent larger frequencies or proportions.
In GCSE Maths, you need to read pie charts and also calculate sector angles from data.
What you should understand after this topic
- Understand why a pie chart represents a whole circle
- Read and compare sectors
- Find sector angles from frequencies
- Find frequencies from sector angles
- Avoid common pie chart mistakes
Key Definitions
Pie Chart
A circular chart split into sectors to show proportions of a whole.
Sector
A slice of the circle representing one category.
Angle
The size of a sector, measured in degrees.
Frequency
The number of items in a category.
Total Frequency
The total number of items represented by the full circle.
Proportion
The fraction or part of the whole belonging to one category.
Key Rules
Whole circle
\(360^\circ\)
Part of a whole
Larger frequency means larger sector angle.
Angle from frequency
\( \text{angle} = \dfrac{\text{frequency}}{\text{total}} \times 360 \)
Frequency from angle
\( \text{frequency} = \dfrac{\text{angle}}{360} \times \text{total} \)
Quick Recognition
Pie chart
Shows proportions of a whole using angles.
Bar chart
Shows frequencies using bar heights.
How to Solve
Step 1: Understand a pie chart
A pie chart shows how a whole is split into parts.
\( \text{Total angle} = 360^\circ \)
Exam tip: All sector angles must add to 360°.
Step 2: Recognise what is given
Given frequencies
Find angles.
Given angles
Find frequencies.
Step 3: Find sector angle
Use this when frequencies are given.
\( \text{Angle} = \dfrac{\text{frequency}}{\text{total}} \times 360 \)
Exam thinking: Convert proportion into degrees.
Step 4: Find frequency from angle
Use this when angles are given.
\( \text{Frequency} = \dfrac{\text{angle}}{360} \times \text{total} \)
Step 5: Compare sectors
Larger angles represent larger values.
Bigger angle
Bigger frequency.
Equal angles
Equal values.
Step 6: Drawing a pie chart
Exam tip: Always show working for angles.
- Find the total frequency.
- Convert each value into an angle.
- Draw a circle.
- Measure each angle with a protractor.
- Label clearly or add a key.
Step 7: Common mistakes
Wrong total
Forgetting total is 360°.
Incorrect proportion
Using wrong denominator.
Poor accuracy
Not measuring angles carefully.
Missing labels
Unclear categories.
Step 8: Exam method summary
See pictograms and bar charts for other ways to represent data.
- Identify what is given (angles or frequencies).
- Use correct formula.
- Calculate carefully.
- Check total equals 360°.
- Interpret or draw clearly.
Example Questions
Edexcel
Exam-style questions inspired by Edexcel GCSE Mathematics, focusing on reading pie charts.
Edexcel
The pie chart shows how 40 students travel to school.
One quarter of the students travel by bus. How many students is this?
Edexcel
How many degrees are in a full pie chart?
AQA
Exam-style questions based on the AQA GCSE Mathematics specification, focusing on calculating angles and frequencies.
AQA
The total frequency is 40. A category has frequency 10.
Find the angle of the sector representing this category.
AQA
The total frequency is 60. A sector has angle \(120^\circ\).
Find the frequency represented by this sector.
AQA
A student says, "All angles in a pie chart must add up to 360°."
Tick one box. True ☐ False ☐
Give a reason for your answer.
OCR
Exam-style questions aligned with OCR GCSE Mathematics, emphasising reasoning and completing pie charts.
OCR
A pie chart has sectors of \(90^\circ\), \(120^\circ\) and \(60^\circ\).
Find the size of the missing angle.
OCR
The pie chart represents 80 people. A sector has angle \(72^\circ\).
Find how many people this sector represents.
OCR
Explain what a larger sector represents in a pie chart.
Exam Checklist
Step 1
Check the total frequency or total angle given.
Step 2
Use the correct formula for angle or frequency.
Step 3
Remember the full circle is \(360^\circ\).
Step 4
Check whether the answer is sensible compared with the size of the sector.
Most common exam mistakes
Total mistake
Using the wrong total frequency.
Angle mistake
Forgetting to multiply or divide by \(360\).
Reading mistake
Guessing from the picture instead of calculating exactly.
Drawing mistake
Measuring sector angles inaccurately with the protractor.
Common Mistakes
These are common mistakes students make when working with pie charts in GCSE Maths.
Forgetting the full circle is 360°
Incorrect
A student uses an incorrect total when calculating sector angles.
Correct
A full pie chart represents 360°. All sector angles must add up to 360°.
Using the wrong total frequency
Incorrect
A student calculates angles using an incorrect total.
Correct
Always find the total frequency first. Each sector angle is calculated using \(\frac{\text{category}}{\text{total}} \times 360\).
Confusing angles and frequencies
Incorrect
A student treats the angle as if it is the frequency.
Correct
Angles represent proportions. To find frequency from an angle, you must reverse the calculation using the total.
Poor rounding of angles
Incorrect
A student rounds angles too early or inaccurately when drawing.
Correct
Calculate angles accurately and round only when necessary. Ensure the total still adds up to 360°.
Judging by appearance instead of calculating
Incorrect
A student estimates answers visually without calculation.
Correct
Always use calculations to find exact values. The size of a sector can be misleading by eye.
Try It Yourself
Practise interpreting and constructing pie charts.
Foundation
Foundation Practice
Interpret pie charts and understand proportions.
A pie chart sector is 180°. What fraction of the whole is this?
Total is 360°.
180 ÷ 360 = 1/2.
What is the total angle in a pie chart?
Full circle.
A full circle is 360°.
A sector is 90°. What fraction is this?
Divide by 360.
90 ÷ 360 = 1/4.
A sector represents 1/3 of the data. What angle is this?
Multiply 1/3 × 360.
1/3 × 360 = 120°.
A sector is 72°. What fraction is this?
Divide by 360.
72 ÷ 360 = 1/5.
Why are pie charts useful?
Think parts of whole.
Pie charts show proportions.
A sector is 45°. What fraction is this?
45 ÷ 360.
45 ÷ 360 = 1/8.
A student uses 180° as total instead of 360°. What is wrong?
Full circle.
Total must be 360°.
A sector is 36°. What fraction is this?
Divide by 360.
36 ÷ 360 = 1/10.
Higher
Higher Practice
Construct and interpret pie charts using data and angles.
A group has 40 students. 10 prefer maths. What angle represents this group?
10/40 × 360.
1/4 × 360 = 90°.
A group has 50 people. 20 choose option A. Find the angle for A.
20/50 × 360.
0.4 × 360 = 144°.
A sector is 108°. What percentage is this?
108 ÷ 360 × 100.
108/360 = 0.3 → 30%.
A sector represents 25% of data. Find its angle.
25% of 360.
0.25 × 360 = 90°.
A pie chart sector is 54°. What fraction is this?
Simplify 54/360.
54/360 = 3/20.
A class has 30 students. 12 choose science. Find the angle.
12/30 × 360.
0.4 × 360 = 144°.
Why must all angles add to 360°?
Complete whole.
360° = full circle.
A sector is 162°. What percentage is this?
162 ÷ 360 × 100.
162/360 = 0.45 → 45%.
A student forgets to convert fraction before finding angle. What is wrong?
Conversion needed.
Must convert correctly.
A group has 80 people. 20 choose option B. Find the angle.
20/80 × 360.
1/4 × 360 = 90°.
Games
Practise this topic with interactive games.
Games coming soon.
Frequently Asked Questions
What does a pie chart show?
Proportions of a whole.
How do I find angles?
Use fraction × 360.
What must total be?
360 degrees.