How to Interpret Pie Graphs? (+FREE Worksheet!)

How to interpret pie graphs, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

A pie graph (also called a circle graph or pie chart) shows how a whole is divided into parts. Each slice of the circle represents a category, and the size of each slice is proportional to that category’s share of the total. Pie graphs are one of the most common ways to display data in Algebra 1 and in everyday life. This lesson shows you how to read and create a pie graph, with worked examples and practice problems.

What Is a Pie Graph?

A pie graph is a circular chart divided into sectors (slices). The entire circle represents 100% of a data set, or 360° total. Each sector’s central angle is proportional to its percentage of the whole. Because each slice must fit inside the circle, all percentages must add up to exactly 100%.

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How to Read and Create a Pie Graph

Reading a Pie Graph

To read a pie graph, identify each labeled slice and its percentage (or fraction). The larger the slice, the larger that category’s share.

Quick example: A pie graph shows favorite sports: Basketball 40%, Soccer 25%, Baseball 20%, Other 15%. The most popular sport is Basketball (largest slice).

Finding the Central Angle for Each Slice

To build or verify a pie graph, convert each percentage to a central angle:

Central \(\color{blue}{\text{ angle } = (\text{ percentage } &\text{ div }; 100) \times 360}\)°

Quick example: A category that is 25% of the total: \(\color{blue}{(25 &\text{ div }; 100) \times 360}\)° = 90°

Finding a Category’s Count from a Pie Graph

If you know the total number of items and a category’s percentage, multiply:

\(\color{blue}{\text{ Count } = \text{ percentage } \times \text{ total }}\)

Quick example: 30% of 200 students chose Math: \(\color{blue}{0.30 \times 200 = 60}\) students.

Step-by-Step Summary

1. Identify all categories and their percentages. Confirm they total 100%.
2. To find the central angle for a slice: \(\color{blue}{(\text{ percentage } &\text{ div }; 100) \times 360}\)°.
3. To find the count for a category: percentage \(\color{blue}{(\text{ as a decimal }) \times \text{ total }}\) count.
4. To find a percentage from a count: \(\color{blue}{(\text{ category count } &\text{ div }; \text{ total count }) \times 100}\).

Watch: Reading Pie Graphs (Video Lesson)

Khan Academy explains how to read and interpret pie graphs (circle graphs) step by step:

Pie Graph – Worked Examples

Example 1: A pie graph shows how 400 students travel to school: Car 35%, Bus 40%, Walk 15%, Bike 10%. How many students take the bus?

\(\color{blue}{\text{ Count } = 0.40 \times 400}\) = 160 students

Example 2: A school surveyed 300 students about their favorite subject. Results: Math 90, Science 75, English 60, History 45, Art 30. What central angle represents Math?

Math \(\color{blue}{\text{ percentage } = 90}\) ÷ \(\color{blue}{300 = 0.30 = 30}\)%
Central \(\color{blue}{\text{ angle } = 0.30 \times 360}\)° = 108°

Example 3: Use the data from Example 2 to find the central angle for Science, English, History, and Art.

Science: \(\color{blue}{(75 &\text{ div }; 300) \times 360 = 0.25 \times 360}\) = 90°
English: \(\color{blue}{(60 &\text{ div }; 300) \times 360 = 0.20 \times 360}\) = 72°
History: \(\color{blue}{(45 &\text{ div }; 300) \times 360 = 0.15 \times 360}\) = 54°
Art: \(\color{blue}{(30 &\text{ div }; 300) \times 360 = 0.10 \times 360}\) = 36°
Check: \(\color{blue}{108 + 90 + 72 + 54 + 36 = 360}\)° ✓

Example 4: A pie graph shows a family’s monthly budget. Housing takes up 120° of the circle. What percentage of the budget goes to housing?

\(\color{blue}{\text{ Percentage } = (120 &\text{ div }; 360) \times 100 = (\frac{1}{3}) \times 100}\) ≈ 33.3%

More Practice: Creating Circle Graphs (Video Lesson)

Mr. Slope Guy demonstrates how to set up and read circle graphs with additional worked examples:

Exercises: Pie Graph

1. A pie graph shows 500 people’s favorite season: Summer 45%, Fall 25%, Winter 20%, Spring 10%. How many people chose Summer?
2. A central angle measures 72°. What percentage of the whole does this slice represent?
3. In a class of 40 students, 16 prefer pizza. What central angle represents this on a pie graph?
4. Five categories take up the following central angles: 100°, 80°, 60°, 70°, and 50°. Do these form a complete pie graph? Show work.
5. A pie graph shows monthly expenses: Rent 35%, Food 25%, Transport 15%, Entertainment 10%, Savings 15%. If total expenses are $2,400, how much is spent on Food?

Answers

1. \(\color{blue}{0.45 \times 500}\) = 225 people
2. \(\color{blue}{(72 &\text{ div }; 360) \times 100}\) = 20%
3. \(\color{blue}{(16 &\text{ div }; 40) \times 360 = 0.40 \times 360}\) = 144°
4. \(\color{blue}{100 + 80 + 60 + 70 + 50 = 360}\)° → Yes, they form a complete pie graph.
5. 0.25 × $2,400 = $600

Want More Practice?

We haven’t published a worksheet built specifically for Pie Graph just yet. In the meantime, the free worksheets below cover closely related skills and concepts. If you’d like extra practice, download any that look helpful, complete the problems, and check your work. They’re a great way to reinforce what you learned on this page and strengthen the foundations this topic builds on:

• Download Displaying Data with Histograms Worksheet
• Download Two Way Frequency Tables Worksheet
• Download Measures of Center and Spread Worksheet

Frequently Asked Questions

What is a pie graph?

A pie graph, also called a circle graph, is a circle divided into slices that show how a whole is split into parts. Each slice stands for one category, and its size matches that category’s share of the total, so all the slices add up to 100%. A pie graph of a family’s monthly budget, for example, shows what fraction goes to rent, food, and savings.

Is a pie graph the same as a pie chart?

Yes. Pie graph, pie chart, and circle graph all name the same display: a circle cut into sectors that show parts of a whole. Math textbooks and state tests often say circle graph, while spreadsheet programs usually say pie chart. The way you read and build each one is exactly the same.

How do you make a pie graph?

Find each category’s percent of the total, then multiply that percent by 360° to get the angle of its slice. If 10 of 40 students choose soccer, that is 25%, and 0.25 × 360° = 90°. Draw each angle from the center with a protractor, label the slices, and check that the angles add up to 360°.

How do you solve pie graph problems?

Turn the slice into a percent or fraction, then multiply by the total. If a pie graph shows that 30% of 200 surveyed students walk to school, then 0.30 × 200 = 60 students walk. To work backward from an angle, divide by 360°: a 72° slice is 72/360 = 1/5 of the whole, or 20%.

What is a pie chart used for?

A pie chart is used to compare parts of one whole, especially when there are only a few categories. It works well for questions like what share of a class prefers each lunch option. It is a poor choice for showing change over time or for comparing many small categories, where a bar graph or line graph is easier to read.

Is a pie chart qualitative or quantitative?

A pie chart displays qualitative, or categorical, data: each slice is a category like a color, a sport, or a type of expense. The numbers behind it are the counts or percents for those categories. If your data is a set of measurements, such as heights, a histogram or dot plot is the better choice.

Related Topics

• Mean, Median, Mode, and Range
• Scatter Plots
• Probability Problems
• Data and Graphs
• Statistics