Pie Charts
A pie chart is a circular chart that shows how a total is split between categories, with each category drawn as a sector whose angle is proportional to its frequency, found using (category frequency / total frequency) x 360, since a full turn is 360 degrees. Pie charts show proportions clearly, but unlike bar charts do not show exact frequencies unless the sectors are labelled, so converting between frequencies and angles, and drawing or measuring sectors accurately with a protractor, are the core skills.
Before you start
Make sure you're comfortable with these topics first:
Method
- Find the total frequency by adding up all the categories, or use the total given in the question.
- To find the angle for a category, divide its frequency by the total frequency, then multiply by 360 degrees.
- Check that all the angles add up to 360 degrees - this is a useful check on your working before drawing.
- To draw the pie chart, use a protractor to mark each angle in turn from the centre, measuring each new sector from the edge of the previous one rather than always from the same starting line.
- To work backwards from an angle to a frequency, divide the sector's angle by 360, then multiply by the total frequency.
- If the total is not given, use one known category's frequency and angle to find the value of 1 degree (frequency / angle), then multiply by 360 to find the total, or by another sector's angle to find its frequency.
Worked example
A survey asked 90 pupils to name their favourite school subject. The results were: Maths 27 pupils, Science 18 pupils, Art 15 pupils, and the rest chose English. Draw a pie chart to show this information, stating each sector's angle.
- Find the number who chose English: 90 - (27 + 18 + 15) = 90 - 60 = 30 pupils.
- Divide each frequency by the total, 90, to find the fraction of the circle it takes up.
- Multiply each fraction by 360 degrees: Maths = 27/90 x 360 = 108 degrees.
- Science = 18/90 x 360 = 72 degrees. Art = 15/90 x 360 = 60 degrees. English = 30/90 x 360 = 120 degrees.
- Check the angles total 360 degrees: 108 + 72 + 60 + 120 = 360, confirming the working is correct.
Practice questions
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Q1A pie chart shows how 72 people travel to work. The sector for 'Car' has an angle of 150 degrees. How many people travel by car?Show answer
Answer: 30 people (150/360 x 72)
Q2In a survey of 40 pupils' favourite fruit, 8 chose banana. What angle should be drawn for the 'banana' sector of a pie chart?Show answer
Answer: 72 degrees (8/40 x 360)
Q3A pie chart divides 300 customers between three shops: Shop A 90 degrees, Shop B 150 degrees, Shop C the rest. How many customers use Shop C?Show answer
Answer: 100 customers (Shop C's angle is 360 - 90 - 150 = 120 degrees, so 120/360 x 300 = 100)
Q460 students are asked to choose their favourite colour. The frequencies are: Blue 21, Red 15, Green 9, Yellow 15. Calculate the angle for the 'Blue' sector.Show answer
Answer: 126 degrees (21/60 x 360)
Q5A pupil calculates the four sector angles of a pie chart as 95, 120, 80 and 60 degrees. Explain how you know at least one angle must be wrong, without knowing what the categories are.Show answer
Answer: The four angles of a pie chart must add up to 360 degrees, but 95 + 120 + 80 + 60 = 355, not 360, so at least one angle is incorrect
Q6A pie chart showing 50 people's pet ownership has a 'no pets' sector of 72 degrees. How many of the 50 people have no pets?Show answer
Answer: 10 people (72/360 x 50)
Q7In a pie chart, the 'Football' sector represents 24 people and has an angle of 96 degrees. Find the total number of people surveyed.Show answer
Answer: 90 people (24 people is worth 96 degrees, so 1 degree is worth 24/96 = 0.25 people, and 360 degrees is worth 0.25 x 360 = 90 people)
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
A pie chart shows the results of a survey of 120 people's preferred holiday type. The angles are: Beach 150 degrees, Mountains 120 degrees, City the remainder. (a) Find the angle for the City sector. (b) Work out how many people chose City.
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In a pie chart showing how 45 pupils travel to school, the Walk sector has an angle of 168 degrees, and the Bus sector has an angle of 104 degrees. The rest of the pupils cycle. (a) Work out how many pupils walk to school. (b) Work out how many pupils cycle to school.
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Two schools carried out the same survey asking pupils how they travel to school. The results are shown as two pie charts side by side: School A's circle is drawn much larger than School B's circle, and both have a Walk sector of exactly 90 degrees. A reader says 'School A's circle is bigger, and both Walk sectors are a quarter of their circle, so School A has more pupils who walk than School B.' Explain why the reader cannot be sure this is correct, and state what extra information is needed to compare the two schools properly.
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Free printable worksheet
Want more practice on paper? Download the pie charts worksheet pack - 5 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 34 of KS3 Maths Workbook 2, the whole course as one free printable PDF.
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