Showing parts of a whole
A circle graph (pie chart) shows how a whole is divided into parts. Each category is a sector (slice). The bigger the slice, the bigger the share.
Circle graphs are best when:
- The data adds up to a whole (100%).
- There are a few categories (about 2 to 7).
- You want to compare each part with the whole.
The key fact
A full circle is 360° and represents 100%.
| Percent | Central angle |
|---|---|
| 50% | 180° |
| 25% | 90° |
| 10% | 36° |
| 1% | 3.6° |
Making a circle graph
Data: How 40 students get to school.
| Method | Students | Fraction | Percent | Central angle |
|---|---|---|---|---|
| Walk | 14 | 14/40 | 35% | 0.35 × 360 = 126° |
| Bus | 12 | 12/40 | 30% | 108° |
| Car | 10 | 10/40 | 25% | 90° |
| Bike | 4 | 4/40 | 10% | 36° |
| Total | 40 | 1 | 100% | 360° |
Steps:
- Find each category’s fraction of the total.
- Change it to a percent.
- Multiply each fraction by 360° to get its central angle.
- Check the angles add to 360°.
- Draw a circle, mark the centre, and use a protractor to draw each angle.
- Label each sector or add a legend, and give the graph a title.
Reading a circle graph
If a graph shows a budget of $2,000 and "Rent" is 40%, the rent is 0.40 × 2,000 = $800.
If a sector’s angle is 72°, its percent is 72/360 = 0.2 = 20%.
When not to use a circle graph
- Data that changes over time → use a line graph.
- Categories that don’t add up to a whole (like survey questions where people choose several answers).
- Lots of tiny categories → a bar graph is clearer.
Worked examples
Example 1: A sector is 15% of the graph. Central angle?
0.15 × 360 = 54°.
Example 2: A sector has central angle 90°. What percent?
90/360 = 25%.
Example 3: 30 people were surveyed and 12 chose pizza. Central angle for pizza?
12/30 × 360 = 144°.
Common mistakes
- Using percent numbers as degrees (drawing 35° for 35%).
- Angles that don’t add to 360° because of rounding. Adjust the largest slightly.
- Using circle graphs for data that isn’t parts of a whole.
Try it yourself
- What central angle shows 40%?
- A sector is 54°. What percent is that?
- Of 60 students, 15 prefer art. Find the percent and angle.
- Why isn’t a circle graph good for monthly temperatures?
Answers: 1) 144° 2) 15% 3) 25%, 90° 4) Temperatures change over time and don’t add up to a whole.
Quick recap
- A circle graph shows parts of a whole; 100% = 360°.
- Central angle = fraction × 360°.
- Label each sector and include a legend and title.