A pie chart represents data as slices of a circle. Each slice (sector) has an angle proportional to the frequency or percentage it represents, so the whole chart adds up to 360°. To read a pie chart, find the sector angle and use the proportion 360° represents the total.
Why pie charts use 360°
A full circle = 360°. Every piece of data in a pie chart is shown as a fraction of that full circle. The sector angle for any category is:
sector angle = (frequency ÷ total frequency) × 360°
How to read (interpret) a pie chart
Step 1 — read the sector angle
Use the protractor markings on the chart, or the angle given in the question.
Step 2 — set up the proportion
The full 360° represents the total number of items. So:
frequency for that sector = (sector angle ÷ 360°) × total
Step 3 — calculate
Substitute the values and work out the answer.
Worked example 1 — finding a frequency from a pie chart
A survey of 120 pupils asked about their favourite sport. The "football" sector has an angle of 90°. How many pupils chose football?
frequency = (90 ÷ 360) × 120 = ¼ × 120 = 30 pupils
Worked example 2 — finding a sector angle from a frequency table
The table below shows the favourite subjects chosen by 40 pupils. Calculate the sector angle for each subject.
| Subject | Frequency | Calculation | Sector angle |
|---|---|---|---|
| Maths | 10 | (10 ÷ 40) × 360° | 90° |
| English | 8 | (8 ÷ 40) × 360° | 72° |
| Science | 14 | (14 ÷ 40) × 360° | 126° |
| History | 8 | (8 ÷ 40) × 360° | 72° |
| Total | 40 | 360° |
Always check that the sector angles add to 360°: 90 + 72 + 126 + 72 = 360°. ✓
How to draw a pie chart — step by step
Step 1 — calculate sector angles
Use the formula: sector angle = (frequency ÷ total) × 360°
Step 2 — draw a circle
Use a compass to draw a neat circle of a reasonable size (radius about 4–5 cm is ideal in exam conditions).
Step 3 — draw the first sector
Draw a radius line from the centre to the 12 o'clock position (straight up). Place your protractor on the centre, align 0° to the radius line, and mark the angle for the first category. Draw a second radius to that mark.
Step 4 — continue round the chart
Use the last radius as the new base line for each subsequent sector. Continue until all sectors are drawn.
Step 5 — label each sector
Write the category name and/or angle inside each sector, or use a key.
Worked example 3 — interpreting a pie chart with percentages
A pie chart shows that 45% of a class prefer science. If the class has 60 pupils, how many prefer science?
Method 1 (percentage): 45% of 60 = (45 ÷ 100) × 60 = 27 pupils
Method 2 (angle check): 45% → sector angle = 0.45 × 360° = 162°
Both approaches give the same answer. ✓
Common mistakes with pie charts
| Mistake | Effect | How to avoid |
|---|---|---|
| Forgetting that angles must sum to 360° | Chart looks wrong or gaps appear | Always add up angles before drawing |
| Using 100 instead of 360 in the formula | Wrong angles | Remember: circle = 360°, not 100° |
| Starting each sector from the previous mark's start, not end | Sectors overlap | Use the last drawn line as your new baseline |
| Not labelling sectors | Marks lost in exams | Always add category labels or a key |
Pie charts in the national curriculum
The DfE's KS3 mathematics programme of study requires pupils to construct and interpret appropriate tables, charts, and diagrams, including pie charts for categorical data. The statutory national curriculum for Key Stage 3 and 4 confirms that both drawing and interpreting pie charts are assessed in the statistics strand of KS3 and GCSE maths, including questions that require pupils to calculate missing frequencies from sector angles.
Frequently asked questions
How do I find the total frequency from a pie chart?
If you know the frequency for one sector and its angle, you can find the total: total = (frequency ÷ sector angle) × 360°. For example, if 15 people chose red and the red sector is 60°, total = (15 ÷ 60) × 360 = 90 people.
What if my sector angles do not add up to 360°?
Rounding during the calculation often causes the angles to add to 359° or 361°. Adjust the largest sector by 1° to correct the total. Always show your check in exam work: examiners award a method mark for demonstrating you verified the sum equals 360°.
Can a pie chart show continuous data?
Pie charts are best suited to categorical (non-numerical) data, such as favourite colours or types of transport. They are less useful for continuous data (like heights or times), where bar charts or histograms are more informative. At KS3, exam questions typically use pie charts for categorical data only.
How is a pie chart different from a bar chart?
A bar chart shows frequency on an axis, so you can read off exact values easily. A pie chart shows proportions (shares of the whole), making it easy to compare relative sizes — but harder to read exact frequencies without calculation. Use a pie chart when the key message is the proportion each category makes up of the total.
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