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

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

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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 the difference between a pie graph and a bar graph?

A pie graph (circle graph) shows parts of a whole as slices, making it ideal when you want to visualize percentages or proportions. A bar graph compares separate categories using bars, making it better for comparing individual values side by side.

How do all the slices of a pie graph relate to each other?

All slices must add up to the complete circle: 100% or 360°. If any slice is missing or incorrectly sized, the total will not equal 100% or 360°, and the pie graph is wrong.

Can a pie graph show negative values?

No. Pie graphs can only display non-negative values because a slice cannot have negative size. If your data include negative values, use a different type of graph such as a bar graph or line graph.

Related Topics

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