3.6 Pie Charts

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: working out angles, drawing pie charts and reading information from them. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

• Work out the angles for a pie chart from a frequency table
• Draw a pie chart accurately with a protractor
• Work out frequencies, fractions and percentages from a pie chart
• Compare pie charts and explain why sector size is not the same as frequency

Key words

• Pie chart: A circle split into sectors to show how a whole is shared out.
• Sector: A "slice" of the pie chart. Its angle is in proportion to the frequency.
• Angle per item: 360° ÷ total frequency: the angle that stands for one person or item.
• Protractor: An instrument for measuring and drawing angles in degrees.

Working out the angles

A full circle is 360°. Find the total frequency, work out 360° ÷ total to get the angle for one item, then multiply by each frequency.

Worked example: holiday destinations of 40 people

Total = 15 + 8 + 12 + 5 = 40, so each person is 360° ÷ 40 = 9°.
Spain 15 × 9 = 135°, France 8 × 9 = 72°, UK 12 × 9 = 108°, Italy 5 × 9 = 45°
Check: 135 + 72 + 108 + 45 = 360 ✓

Answer: 135°, 72°, 108°, 45°

• Spain; Frequency 15; Angle 15 × 9 = 135°
• France; Frequency 8; Angle 8 × 9 = 72°
• UK; Frequency 12; Angle 12 × 9 = 108°
• Italy; Frequency 5; Angle 5 × 9 = 45°
• Total; Frequency 40; Angle 360°

Key fact: The angles must add up to 360°. Always check before you draw.

Drawing a pie chart

Draw a circle and a radius (a line from the centre to the edge). Put the centre of the protractor on the centre of the circle and measure the first angle from the radius. Draw the next angle from the line you just drew. Label every sector or give a key.

Worked example: checking accuracy

You only need to measure three of the four angles.
The last sector should then be 45°: measure it as a check. If it is out by more than 2°, look for an error.

Answer: measure 135°, 72° and 108°; Italy is what is left (45°)

Reading a pie chart

To find a frequency from an angle, find what one degree (or one person) is worth. The fraction of the whole is angle ÷ 360.

Worked example: total is known

120 people are shown by 360°, so 1 person = 360 ÷ 120 = 3°.
Films: 150 ÷ 3 = 50 people. Sport: 60 ÷ 3 = 20 people.
Fraction who chose news = 90/360 = 1/4.

Answer: films 50, sport 20, news 1/4 of the people

Worked example: total is not known

In another pie chart, a sector of 80° stands for 24 people. How many people are there altogether?
The whole circle is 360 ÷ 80 = 4.5 times as big as the sector.
So the total is 4.5 times as many people: 4.5 × 24 = 108.

Answer: 108 people

Comparing pie charts

A pie chart shows proportions, not numbers. If two pie charts have different totals, a bigger sector does not always mean a bigger frequency.

Worked example: which class has more footballers?

Class A: 144/360 × 30 = 12 students.
Class B: 108/360 × 60 = 18 students.

Answer: Class B has more, even though its football sector is smaller

Common mistakes

• Using 100 instead of 360, or forgetting to divide 360 by the total.
• Angles that do not add up to 360°: check before drawing.
• Saying a bigger sector means more people when the two pie charts have different totals.
• Measuring from the wrong scale on the protractor (e.g. drawing 135° instead of 45°).

Revision questions

Try these, then check your answers below each one.

Question 1. A pie chart shows the favourite sports of 72 people. What angle represents one person?

Answer: 5 °

Working: 360 ÷ 72 = 5°.

Question 2. In the same pie chart (72 people), 18 people chose tennis. What is the angle of the tennis sector?

Answer: 90 °

Working: 18 × 5 = 90°.

Question 3. A pie chart shows the views of 90 people. The sector for "yes" has an angle of 120°. How many people said yes?

Answer: 30

Working: 120/360 = 1/3, and 1/3 of 90 is 30.

Related lessons

• Previous lesson: 3.5 Stem and Leaf Diagrams
• Next lesson: 3.7 Scatter Graphs
• In this chapter: 3.1 Frequency Tables
• In this chapter: 3.2 Two-way Tables
• In this chapter: 3.3 Representing Data

Continue in the full course

This lesson is section 3.6 (EGCMF0306) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.