Pie Chart (Pie Graph) — Definition, Formula & Examples

A pie chart is a circle divided into slices where each slice represents a category's share of the whole. The bigger the slice, the larger that category's portion of the total.

A pie chart is a circular statistical graphic partitioned into sectors whose arc lengths (and consequently areas) are proportional to the quantities they represent, with the full circle corresponding to 100% of the data.

Key Formula

\text{Slice angle} = \frac{\text{category value}}{\text{total}} \times 360°

Where:

$\text{category value}$ = The count or amount for one category
$\text{total}$ = The sum of all category values
$360°$ = The full rotation of the circle

How It Works

Each category in your data gets a slice of the circle. To find the size of a slice, divide the category's value by the total, then multiply by 360° to get the angle. You can also express each slice as a percentage by multiplying the fraction by 100. Slices should add up to exactly 360° or 100%. Pie charts work best when you have a small number of categories (roughly 2 to 6) and want to emphasize how each part compares to the whole.

Worked Example

Problem: A class voted on their favorite fruit: Apples = 10, Bananas = 6, Grapes = 4. Draw the pie chart angles for each fruit.

Find the total: Add all the votes together.

10 + 6 + 4 = 20

Apples slice: Divide Apples by the total and multiply by 360°.

\frac{10}{20} \times 360° = 180°

Bananas slice: Repeat for Bananas.

\frac{6}{20} \times 360° = 108°

Grapes slice: Repeat for Grapes.

\frac{4}{20} \times 360° = 72°

Answer: Apples gets a 180° slice (50%), Bananas gets 108° (30%), and Grapes gets 72° (20%). The three angles sum to 360°.

Visualization

Why It Matters

Pie charts appear in newspapers, science reports, and business presentations whenever someone wants to show how a total breaks into parts. Learning to read and create them builds a foundation for data literacy you will use in statistics courses, social studies, and everyday decision-making.

Common Mistakes

Mistake: Making slices that do not add up to 100% (or 360°) because a category was left out or values were rounded carelessly.

Correction: Always check that your percentages sum to 100% and your angles sum to 360°. If rounding causes a small gap, adjust the largest slice by 1° to compensate.