Create pie charts by calculating angles to represent data proportionally
A pie chart is a circular chart divided into sectors, where each sector represents a proportion of the whole. The size of each sector (its angle) is proportional to the quantity it represents. Since a complete circle has 360°, you calculate angles by finding what fraction each value is of the total, then multiplying by 360°.
Pie charts make it easy to see proportions and compare parts of a whole at a glance.
Used everywhere from business presentations to scientific reports to show how data is distributed.
Combines fractions, percentages, angles, and proportional reasoning in a practical context.
A survey of 40 pupils: Football (20), Basketball (10), Tennis (6), Swimming (4)
Total: 40 pupils
Football: 20/40 × 360° = 180°
Basketball: 10/40 × 360° = 90°
Tennis: 6/40 × 360° = 54°
Swimming: 4/40 × 360° = 36°
Check: 180° + 90° + 54° + 36° = 360° ✓
60 students: Walk (24), Bus (18), Car (12), Cycle (6)
Total: 60 students
Walk: 24/60 × 360° = 144°
Bus: 18/60 × 360° = 108°
Car: 12/60 × 360° = 72°
Cycle: 6/60 × 360° = 36°
Check: 144° + 108° + 72° + 36° = 360° ✓
90 families: Dogs (36), Cats (27), Fish (18), Other (9)
Total: 90 families
Dogs: 36/90 × 360° = 144°
Cats: 27/90 × 360° = 108°
Fish: 18/90 × 360° = 72°
Other: 9/90 × 360° = 36°
Check: 144° + 108° + 72° + 36° = 360° ✓
Library has 120 books: Fiction (60), Non-fiction (30), Mystery (20), Science (10)
Total: 120 books
Fiction: 60/120 × 360° = 180°
Non-fiction: 30/120 × 360° = 90°
Mystery: 20/120 × 360° = 60°
Science: 10/120 × 360° = 30°
Check: 180° + 90° + 60° + 30° = 360° ✓
Learn from typical errors students make and discover how to avoid them!
What students often do wrong:
Students confuse percentages with angles and multiply by 100 instead of 360, or forget that a full circle is 360 degrees, not 100.
Correct approach: Remember that angles in a circle always total 360°. Calculate each angle as: (value ÷ total) × 360°
Memory tip: "360 for a circle round, that's the total that we've found!"
What students often do wrong:
After calculating all angles, students don't verify that they add up to exactly 360°, missing calculation errors.
Correct approach: Always add all your calculated angles together at the end. They must total exactly 360°. If not, check your calculations!
Memory tip: "Add them up to check your work, angles total 360° - don't shirk!"
When drawing pie charts, start at the 12 o'clock position (top of circle) and work clockwise. Draw the largest sector first - this makes it easier to fit everything in neatly. Use a protractor carefully, measuring from the previous line each time!
You've mastered Constructing Pie Charts!
Next: Learn to calculate the mean average to summarize data sets