Units of Area: The Conversion Ladder, Hectares and Ares
Math Education6 min read
Math Education
7 min read
Pie Charts: How to Draw, Calculate Angles + Examples
Published: 12.08.2026·Updated: 12.08.2026
Dewi Lestari
Mathematics Specialist
A pie chart presents data as a circle divided into sectors, with each sector's size proportional to its share of the data. It is the right choice when the point is parts of a whole, not comparison over time. The topic appears in Year 5 and is developed in Year 8.
The Two Formulas
A pie chart can be expressed in degrees or in percentages.
In degrees (a full circle = 360°):
In percentages (the whole = 100%):
The link between them is simple: 1% = 3.6°, since 360 divided by 100.
Building a Pie Chart
Of 40 students: 12 like football, 10 basketball, 10 volleyball, 8 swimming.
| Sport | Count | Angle | Percentage |
|---|---|---|---|
| Football | 12 | 12/40 × 360 = 108° | 30% |
| Basketball | 10 | 10/40 × 360 = 90° | 25% |
| Volleyball | 10 | 90° | 25% |
| Swimming | 8 | 8/40 × 360 = 72° | 20% |
| Total | 40 | 360° | 100% |
Always check the total row. If the angles do not add to 360° or the percentages to 100%, something is miscalculated. The check is free and catches almost every error before the paper is handed in.
Reverse Questions: From Angle to Data
The form that appears most often in exams is the reverse — the chart is given and the count is asked for.
A pie chart shows the hobbies of 120 students. The "reading" sector is 60°. How many students read?
Rearrange the formula:
frequency = (angle ÷ 360) × total = (60 ÷ 360) × 120 = 20 students
If a percentage is given instead: frequency = percentage × total. For example 25% of 120 = 30 students. See how to calculate percentages.
Finding a Missing Sector
One sector is often left blank on purpose. The key: all sectors total 360° or 100%.
Three sectors are 90°, 120° and 60°. What is the fourth?
360 − 90 − 120 − 60 = 90°
When to Use a Pie Chart
| Purpose | Right chart |
|---|---|
| Showing proportions of a whole | Pie |
| Comparing categories | Bar |
| Showing change over time | Line |
A pie chart is wrong when there are many categories, say more than six — the slices become too thin to tell apart. Choosing the right chart is a skill in itself, and it is precisely what reasoning questions test.
The Mistakes That Actually Cost Marks
1. Using 100 when degrees were asked for. Writing (12/40) × 100 and answering "30 degrees". Read the required unit first — this is the number one cause.
2. Angles not totalling 360°. If the sum is off, a sector is miscalculated. A child can catch this without an answer key.
3. Forgetting to multiply back by the total in reverse questions. Answering "1/6" when the number of students was asked for.
4. Reading a chart by eyeballing the slices. A 90° and a 100° sector are nearly indistinguishable by eye. Always use the printed figures, never the visual.
5. Misreading the protractor while drawing. That is an instrument-reading problem, not a statistics one.
