Pie Charts - Showing Parts of a Whole
A pie chart is a circular chart divided into slices. Each slice represents a category, and the size of the slice is proportional to that category's share of the total. Pie charts are ideal for showing how a whole is divided into parts.
The pie chart was introduced in 1801 by William Playfair, the same Scottish engineer who had already invented the bar chart and line graph fifteen years earlier, in a book called the Statistical Breviary. His very first pie chart divided a circle to show how the land area of the Turkish Empire was split between its territories in Europe, Asia, and Africa – the earliest known use of a circular diagram to represent proportions of a whole. Despite being over 200 years old, the pie chart remains one of the most instantly recognisable chart types today, though modern data analysts often debate its limits: because the human eye is much better at comparing the lengths of bars than the angles of slices, many statisticians now recommend a bar chart instead whenever more than a handful of categories need comparing precisely.
How Pie Charts Work
A full circle = 360 degrees = 100% of the data. Each category's angle is calculated as:
Angle = (Frequency ÷ Total) × 360
Worked Examples
| Subject | Frequency | Calculation | Angle |
|---|---|---|---|
| Maths | 10 | 10/40 × 360 | 90° |
| English | 8 | 8/40 × 360 | 72° |
| Science | 14 | 14/40 × 360 | 126° |
| Art | 8 | 8/40 × 360 | 72° |
| Total | 40 | 360° |
90/360 = 1/4. 1/4 × 200 = 50 people.
135/360 × 80 = 3/8 × 80 = 30 people.
Advantages and Limitations
| Advantages | Limitations |
|---|---|
| Shows proportions clearly at a glance | Hard to compare slices of similar size |
| Good for part-to-whole relationships | Exact values are not easy to read |
| Visually appealing | Not suitable for data with many small categories |
Key Takeaways
- Angle = (Frequency ÷ Total) × 360. All angles must sum to 360°.
- Pie charts show proportions, not exact values – always include a key or label.
- To find a frequency from an angle: Frequency = (Angle ÷ 360) × Total.