# Reading & Interpreting Circle Graphs & Central Angles

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• 0:00 What Is a Circle Graph?
• 0:57 How to Use
• 1:56 Central Angles
• 2:49 How to Build a Circle Graph
• 4:06 Lesson Summary
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Lesson Transcript
Instructor: Kevin Newton

Kevin has edited encyclopedias, taught middle and high school history, and has a master's degree in Islamic law.

Circle graphs are some of the most useful graphical descriptions of data around. However, without knowing how to find central angles, their usefulness is limited, and their creation is difficult. In this lesson, we learn how to find central angles while using and creating circle graphs.

## What Is a Circle Graph?

When trying to present the total proportion out of a whole, circle graphs are ideal. Circle graphs, also called pie graphs or pie charts, quickly show, in a very easy to understand fashion, what proportion of the whole is represented by each type of category listed. As you can imagine, this makes for a very useful graph. Literally everything, from pizza consumption to the spending of national governments, can be portrayed using a circle graph, and, very often, it is.

However, making them is a bit more difficult than it first seems. After all, there are 360 degrees in a circle, but a data set typically has only 100 percentage points. In this lesson, we'll look at not only how to use circle graphs but how central angles help us to draw more accurate graphs. We'll also use what we've learned to create our own circle graphs.

## How to Use Circle Graphs

Again, the beauty of a circle graph is really in how easy it is to read. After all, it's pretty easy to see the impact of a circle graph by looking at the relative sizes of the pieces of one. Even really complicated things are made pretty clear by a circle graph.

Take, for example, government spending. This chart shows the money spent by the United States government over the course of a year (see video). Without getting too political, we can make the statement that the government spent more on Social Security, the biggest chunk of the pie, than it did on the Department of Education, which is one of the small slivers in the upper left corner.

However, it is not just about the relative sizes of the pieces. It's also about the percentage points that very often help to illustrate the data contained with the graph. Using these as well as some value of the whole of the circle, we can quickly figure out pretty accurate quantities for each. In this chart (see video), the percentages seem really precise - but remember, these are out of a budget of more than several trillion dollars.

Drawing a circle graph has one difficulty though. The angles that each area occupies have to be pretty precise for the whole thing to be of any value. Otherwise, it doesn't accurately show information. In order to do this, we have to transform percentages into central angles. Central angles are the measures of the angles taken from the center of the circle to the area it covers.

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