A pie chart is a circle divided into sectors. Each sector represents a category. The size of each sector (its angle) shows the proportion of the total that category represents. A full circle = 360°, so each sector's angle is calculated as:
Check: \(162 + 90 + 72 + 36 = 360°\) ✓ Angles must always add up to 360°.
Example 2 — What does 25% look like on a pie chart?
Step 1
25% of the whole = \(\frac{25}{100} \times 360 = 90°\). So a 25% sector has an angle of 90°.
Step 2
This is exactly one quarter of the circle (\(\frac{1}{4} \times 360 = 90°\)).
Step 3
Useful check: a half = 180°, a quarter = 90°, a third ≈ 120°.
Key point: Pie charts show PROPORTIONS, not exact amounts. Two pie charts with the same sector sizes could represent very different totals. Always note the total \(n\) when interpreting a pie chart.
✓ Quick Check 1 — Pie chart angles and proportions
Question 1 of 10
Drawing Pie Charts — Calculate, Then Draw
To draw a pie chart: first calculate each sector angle using the formula. Then draw a circle, draw a radius, and use a protractor to measure each angle in turn — always measuring from the last line drawn. Label each sector or add a key.
Example 1 — Draw a pie chart for favourite drinks (40 people)
Check: \(132 + 108 + 120 = 360°\) ✓ These work out perfectly here.
Step 3
If angles don't sum to 360° due to rounding, adjust the largest sector by ±1° to compensate.
Common mistake: Measuring the next angle from the original start line each time, rather than from the last drawn line. Always measure each new sector FROM THE PREVIOUS LINE.
✓ Quick Check 2 — Drawing pie charts
Question 1 of 10
Reading and Interpreting Pie Charts
To interpret a pie chart, convert sector angles to fractions or percentages of the whole. If you know the total, you can find the actual number in any sector. The key formulas are:
Real-life context: When comparing two pie charts, look at proportions, not sizes. A "Maths" sector of 90° means one quarter of each group chose Maths — even if one survey had 100 people and the other had 1000.
Interactive — Pie Chart Builder
Presets:
Practice: Pie Chart Angles
Work out each answer. Type your answer, then click Check.
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Question
Answer
Result
1
40 people surveyed. 10 prefer tea. What is the sector angle for tea?
2
A pie chart has sectors 120°, 90°, 60°. What is the 4th sector's angle?
3
60 people surveyed. A sector has angle 90°. How many people does it represent?
4
A pie chart shows 25% as one sector. What is its angle (in degrees)?
5
8 people out of 40 chose blue. What is the sector angle for blue?
6
A sector has angle 180°. What percentage of the total does it represent?
7
30 people surveyed. A sector is 108°. How many people does it represent?
8
A pie chart has 4 equal sectors. What is the angle of each (in degrees)?
9
120 students surveyed. The "Walk" sector is 60°. How many students walk?
10
A sector is 45°. What fraction of the circle is this (as a decimal)?
⚠ Things to Watch Out For
Forgetting angles must total 360°: Always check that all your calculated sector angles add up to exactly 360° before moving on.
Using frequency as the angle directly: You must convert frequency to an angle using \(\frac{\text{frequency}}{\text{total}} \times 360\) — the frequency itself is not the angle.
Protractor misalignment: Line up the protractor's centre point and baseline exactly with the circle's centre and starting radius before measuring each angle.
Confusing angle size with quantity: A bigger sector angle means a bigger proportion of the total — always relate the angle back to what it represents.
Rounding errors adding up: If angles are rounded individually, check the total still comes to 360° — adjust the largest sector slightly if needed.