Pie Chart — Definition, Formula & Examples

A pie chart is a circular graph divided into slices, where each slice represents a category's share of the total. The size of each slice is proportional to the percentage or fraction that category contributes to the whole.

A pie chart is a statistical graphic in which a circle is partitioned into sectors whose central angles are proportional to the relative frequencies (or percentages) of the categories they represent, with the full circle corresponding to 100% of the data.

Key Formula

\theta = \frac{n}{N} \times 360°

Where:

$\theta$ = Central angle of the slice in degrees
$n$ = Value (count or amount) for that category
$N$ = Total of all category values

How It Works

Each category in your data set gets its own slice. To find the central angle for a slice, multiply the category's percentage by 360°. For example, a category that makes up 25% of the data gets a slice with a central angle of 90°. Pie charts work best when you have a small number of categories (typically 2–6) that together account for the entire data set. They are most useful for showing how individual parts compare to the whole, not for comparing values between different data sets.

Worked Example

Problem: A class of 40 students was asked their favorite fruit: 16 chose apples, 10 chose bananas, 8 chose oranges, and 6 chose grapes. Find the central angle for each slice of a pie chart.

Apples: Apples make up 16 out of 40 students.

\theta = \frac{16}{40} \times 360° = 144°

Bananas: Bananas make up 10 out of 40 students.

\theta = \frac{10}{40} \times 360° = 90°

Oranges: Oranges make up 8 out of 40 students.

\theta = \frac{8}{40} \times 360° = 72°

Grapes: Grapes make up 6 out of 40 students.

\theta = \frac{6}{40} \times 360° = 54°

Answer: The slices have central angles of 144° (apples), 90° (bananas), 72° (oranges), and 54° (grapes). Check: 144 + 90 + 72 + 54 = 360°.

Visualization

Why It Matters

Pie charts appear in news articles, business reports, and science presentations whenever someone needs to show how a total breaks down into parts. In middle-school math and science courses, you will use them to summarize survey results, budget breakdowns, and experimental data at a glance.

Common Mistakes

Mistake: Using a pie chart when the categories do not add up to 100% of a single whole.

Correction: Pie charts only make sense when every slice is part of the same total. If your categories overlap or come from different data sets, use a bar chart instead.