Pie Charts GCSE Questions, Worked Examples and Answers

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One circle represents one whole

What you need to know about pie charts

Suppose 60 people answer a travel survey and 15 cycle. A pie chart represents all 60 people with one circle. Cycling gets a quarter of the circle because 15 is a quarter of 60. Each wedge-shaped slice is called a sector, and the number of people in a category is its frequency. A full turn is 360°, so a quarter-circle sector has an angle of 90° at the centre.

Frequency share → angle share

Keep the same share of the whole

If 15 of 60 responses belong to one category, that category is one quarter of the data and receives one quarter of 360°.

Category15 responsesthe part

Data set60 responsesthe whole

Sector15/60 × 360° = 90°same fraction of the circle

The full circle represents the full data set. Each sector receives the same fraction of 360° as its category has of the total frequency.

From problem to method

Typical problems you need to be able to solve

These are the main kinds of question in this topic. Each card first states the problem, then explains how to solve it.

Read a category from a sector

What the problem asks: Find a fraction, percentage or frequency represented by a labelled sector.

How to solve it: Compare the sector angle with 360°. If a total frequency is given, multiply that total by angle ÷ 360.

Calculate a sector angle

What the problem asks: A frequency table is given and a pie chart must be completed or drawn.

How to solve it: Find the total frequency, then calculate frequency ÷ total × 360° for each category.

Find a missing angle

What the problem asks: All but one sector angle are known.

How to solve it: Add the known angles and subtract their sum from 360°.

Find the total or a missing frequency

What the problem asks: One sector links a known angle to a known count, and another value is missing.

How to solve it: Use angle ÷ 360 = frequency ÷ total, or first find the number represented by 1°.

Compare two pie charts

What the problem asks: Two charts summarise data sets of different sizes.

How to solve it: Use each chart’s total as well as its sector angle. The same angle means the same proportion, not necessarily the same number.

A reliable routine

Method for converting frequency to angle

Use this method when a category frequency and the total frequency are known. It works because both frequency ÷ total and angle ÷ 360 describe the same share.

Add every category to find the total frequency.
Write the category as frequency ÷ total.
Multiply that fraction by 360°.
Repeat for the remaining sectors.
Check that all sector angles total 360°.

Check: Use a protractor from the same centre point when drawing. A correct calculation with an inaccurate centre can still produce a misleading chart.

Fully worked

Pie charts GCSE worked examples

Each solution explains the clue, why the method fits and how to check the result.

Example 1

Read a simple fraction

2 marks

Question

Sector A in the diagram is $90^\circ$ . What fraction of the data is in A?

The full circle represents the full data set. Each sector receives the same fraction of 360° as its category has of the total frequency.

Compare the sector with the full $360^\circ$ .

\frac{90}{360}=\frac14

\boxed{\frac14}

Example 2

Find an angle from a frequency

3 marks

Question

In a survey of $80$ people, $20$ choose cycling. Find the cycling sector angle.

Cycling is $20$ out of $80$ .

\frac{20}{80}\times360^\circ

=\frac14\times360^\circ

\boxed{90^\circ}

Example 3

Find a frequency from an angle

3 marks

Question

A $72^\circ$ sector represents red cars in a sample of $150$ cars. How many cars are red?

The sector is $72/360$ of the circle.

\frac{72}{360}\times150

=\frac15\times150

\boxed{30\text{ cars}}

Example 4

Find the total frequency

3 marks

Question

A $126^\circ$ sector represents $35$ students. Find the total number of students.

The same proportion links angle and frequency.

\frac{126}{360}=\frac{35}{T}

T=35\times\frac{360}{126}

\boxed{T=100}

Example 5

Compare equal sectors

3 marks

Question

Two pie charts both have a $72^\circ$ music sector. Chart P represents $180$ people and chart Q represents $300$ people. Which chart represents more people choosing music?

In chart P:

\frac{72}{360}\times180=36

In chart Q:

\frac{72}{360}\times300=60

Although the proportions match, the totals differ.

\boxed{\text{Chart Q, with 60 people}}

10 original questions · total 30 marks

Pie charts GCSE exam-style questions

Try each question before opening its fully worked answer. The difficulty rises through the set.

Before you startAllow about 35 minutes · Show the fraction of 360°, give angles in degrees and check that a complete set of sectors totals 360°. · answers start collapsed

1

Use a quarter-circle sector

2 marks

A $90^\circ$ sector represents a category in a survey of $80$ people. Find the frequency.

Show worked answer

\frac{90}{360}\times80=\frac14\times80=\boxed{20}

2

Convert frequency to angle

3 marks

A club has $60$ members and $18$ play tennis. Find the tennis sector angle.

Show worked answer

\frac{18}{60}\times360^\circ

=0.3\times360^\circ

\boxed{108^\circ}

3

Convert angle to frequency

3 marks

An $84^\circ$ sector represents one category in a data set of $120$ . Find its frequency.

Show worked answer

\frac{84}{360}\times120

=\frac7{30}\times120

\boxed{28}

4

Find a missing sector

2 marks

Four sector angles are $115^\circ$ , $95^\circ$ , $60^\circ$ and $x^\circ$ . Find $x$ .

Show worked answer

115+95+60=270

x=360-270

\boxed{x=90^\circ}

5

Find a percentage

2 marks

What percentage of a pie chart is a $144^\circ$ sector?

Show worked answer

\frac{144}{360}\times100\%

=\boxed{40\%}

6

Compare different totals

3 marks

Chart A represents $120$ people in total and chart B represents $240$ people in total. Each chart has a $60^\circ$ sector. How many people does that sector represent in each chart?

Show worked answer

A $60^\circ$ sector is one sixth of a circle.

120\div6=20

240\div6=40

\boxed{20\text{ in A and }40\text{ in B}}

7

Calculate every drawing angle

4 marks

A survey records A: $12$ , B: $18$ , C: $30$ . Calculate the three sector angles.

Show worked answer

The total is

12+18+30=60

A:\ \frac{12}{60}\times360^\circ=72^\circ

B:\ \frac{18}{60}\times360^\circ=108^\circ

C:\ \frac{30}{60}\times360^\circ=180^\circ

Check: $72+108+180=360$ .

\boxed{72^\circ,\ 108^\circ,\ 180^\circ}

8

Recover the total

3 marks

A sector of $45^\circ$ represents $15$ books. Find the total number of books.

Show worked answer

$45^\circ$ is one eighth of $360^\circ$ .

If one eighth is $15$ , the whole is

15\times8=\boxed{120}

9

Use a ratio of sectors

4 marks

Red, blue and green are in the ratio $2:3:5$ . Find each sector angle and the number choosing blue if the total frequency is $250$ .

Show worked answer

There are $2+3+5=10$ ratio parts.

Each angle part is

360^\circ\div10=36^\circ

So the angles are

72^\circ,\ 108^\circ,\ 180^\circ

Blue is $3/10$ of $250$ .

\frac3{10}\times250=\boxed{75}

10

Complete a two-stage comparison

4 marks

In a pie chart of $240$ journeys, walking has angle $54^\circ$ and cycling has angle $81^\circ$ . How many more journeys are cycling than walking?

Show worked answer

Walking:

\frac{54}{360}\times240=36

Cycling:

\frac{81}{360}\times240=54

Difference:

54-36=\boxed{18\text{ journeys}}

Examiner-style feedback

Common pie charts mistakes

Dividing by a category instead of the total

The denominator of the data fraction must be the total frequency.

Treating angle as frequency

An angle is a share of 360°. Convert it using the total number represented by that chart.

Comparing counts from angle alone

Equal sector angles show equal proportions; the counts can differ when chart totals differ.

Drawing from different centres

Every radius must begin at the exact centre, or the sector angles will not represent the calculated shares.

30-SECOND RECAP

Choose, carry out, check

Translate the wording before you reach for a rule.

The full circle is 360°.
Frequency ÷ total equals angle ÷ 360.
Check all angles total 360°.
Use each chart’s total when comparing counts.

Quick answers

Pie charts FAQ

How do I calculate a pie-chart angle?

Use frequency ÷ total × 360°.

How do I find frequency from an angle?

Use angle ÷ 360 × total frequency.

Do pie-chart angles always total 360°?

Yes, because the complete circle represents the complete data set.

Can two equal sectors represent different frequencies?

Yes, if the two pie charts represent different totals.

Build connected skills

What to revise next

Compare distributions

Box plots

Compare centre and spread using five-number summaries.

Revise box plots

Unequal intervals

Histograms

Use bar area rather than angle to represent frequency.

Revise histograms

Part of a whole

Percentages

Move between fractions, percentages and counts.

Revise percentages

Content standards

Curriculum and rights review

Reviewed 5 September 2026 against DfE content S2 and current Pearson Edexcel, AQA and OCR GCSE Mathematics specifications. All questions and diagrams are original.

Official specification references