A circle graph shows how one whole splits into parts. Each part gets a slice of the circle, and the size of the slice matches the size of the part. Drawing one by hand takes two small calculations, a compass and a protractor. This guide gives you the circle graph formula, works one example all the way from raw counts to percentages to degrees, shows how to draw and read the result, and ends with pie chart examples you can open and change.
What Is a Circle Graph?
A circle graph is the chart most people call a pie chart. Wikipedia’s article on the pie chart gives circle chart as another name, and school textbooks often use circle graph: the CK-12 statistics text files its pie chart lessons in a chapter titled Circle Graphs. Whatever the name, Wikipedia’s description applies: a circular graphic divided into slices to show numerical proportion, where the central angle of each slice is proportional to the quantity it stands for.
The idea is old. According to Wikipedia, the earliest known pie chart is generally credited to William Playfair’s Statistical Breviary of 1801.
The Parts of a Circle Graph
The NCES Kids’ Zone, a student site run by the US National Center for Education Statistics, lists four parts of a pie chart:
- The title, a short explanation of what is in the graph.
- The legend, which tells what each slice represents.
- The source, which says where the information came from.
- The data: each slice represents a different piece of data, as part of 100.
In geometry class the slices have a formal name. Each one is a sector of the circle, and the angle at its point, in the middle of the circle, is its central angle.
What It Can and Cannot Show
The same NCES guide says pie charts show percentages of a whole at a set point in time, and that, unlike bar graphs and line graphs, they do not show changes over time. So a circle graph suits “how did the class vote today?” and does not suit “how did the vote change over three years?”
The Circle Graph Formula
You need two formulas, and they are nearly the same.
- Percentage of a slice = value ÷ total × 100
- Angle of a slice = value ÷ total × 360
Both start with the same fraction, the value divided by the total. One scales the fraction to 100 percent and the other to 360 degrees.
Why 360?
A full turn is 360 degrees. Arnold’s Prealgebra, an open textbook published on LibreTexts, puts it this way: divide a circle into 360 equal increments and each increment is one degree. A slice that holds half of the data gets half of the turn, 180 degrees. A quarter gets 90. Wikipedia states the general rule: since the central angles must add up to 360 degrees, a part that is a fraction Q of the total gets an angle of 360 times Q.
Worked Example: From Counts to Percentages to Degrees
A class of 30 students votes for a favorite pet. These numbers are sample data.
| Pet | Students |
|---|---|
| Dog | 12 |
| Cat | 9 |
| Fish | 5 |
| Bird | 3 |
| Other | 1 |
Step 1: Find the Total
12 + 9 + 5 + 3 + 1 is 30. That matches the class size, so no vote is missing.
Step 2: Turn Each Count Into a Percentage
Divide by 30 and multiply by 100. For dogs, 12 ÷ 30 is 0.4, and 0.4 × 100 is 40 percent.
Step 3: Turn Each Count Into an Angle
Divide by 30 and multiply by 360. For dogs, 0.4 × 360 is 144 degrees. A shortcut for this class: 360 ÷ 30 is 12, so every student is worth 12 degrees.
| Pet | Students | Percentage | Angle |
|---|---|---|---|
| Dog | 12 | 40.0% | 144° |
| Cat | 9 | 30.0% | 108° |
| Fish | 5 | 16.7% | 60° |
| Bird | 3 | 10.0% | 36° |
| Other | 1 | 3.3% | 12° |
| Total | 30 | 100.0% | 360° |
Step 4: Check the Totals
The percentages must add up to 100 and the angles to 360. Here they do: 40 + 30 + 16.7 + 10 + 3.3 is 100, and 144 + 108 + 60 + 36 + 12 is 360. If your totals are far off, a division went wrong. If they are off by a hair, it is rounding, which the next section covers.
Here is the finished graph, with the number of students on each slice.
Favorite pets in a class of 30. The dog slice takes 144 of the 360 degrees, which is 40 percent of the circle. Sample data.
Show the data
| Slice | Value |
|---|---|
| Dog | 12 |
| Cat | 9 |
| Fish | 5 |
| Bird | 3 |
| Other | 1 |
And here is the same graph labeled with percentages to one decimal place.
The same circle graph with percentage labels. Fish is 16.7 percent because 5 divided by 30 does not come out even. Sample data.
Show the data
| Slice | Value |
|---|---|
| Dog | 12 |
| Cat | 9 |
| Fish | 5 |
| Bird | 3 |
| Other | 1 |
When Rounding Breaks the Totals
Fractions such as thirds never come out even. Take 9 votes split 4, 3 and 2. The percentages are 44.4, 33.3 and 22.2, which add up to 99.9. Nothing is wrong. Wikipedia’s worked example has the same thing: its rounded columns total 99.9 and 360.2, with a note that the totals do not add up to 100 and 360 because of rounding.
Two habits keep the error small:
- Work out each angle from the original count, not from a rounded percentage. For the slice of 4 votes, 4 ÷ 9 × 360 is exactly 160 degrees. Starting from a rounded 44 percent gives 158.4 degrees, almost 2 degrees short.
- If rounded angles add up to 359 or 361, adjust the largest slice by one degree. Nobody can see one degree on the biggest slice. That adjustment is our own practical advice, not a formal rule.
Going the Other Way
Homework and tests often hand you the graph and ask for the numbers.
From Percentages to Degrees
Multiply the percentage by 3.6, because 360 ÷ 100 is 3.6. A monthly budget given as percentages converts like this:
| Category | Percentage | Angle |
|---|---|---|
| Rent | 35% | 126° |
| Food | 20% | 72° |
| Transport | 15% | 54° |
| Fun | 12% | 43.2° |
| Savings | 10% | 36° |
| Other | 8% | 28.8° |
The angles add up to 360.
From Degrees to Percentages
Divide the angle by 360 and multiply by 100. A slice of 90 degrees is 90 ÷ 360 × 100, which is 25 percent. A slice of 54 degrees is 15 percent.
From an Angle to a Count
If you know the total, a slice’s angle gives you its count: angle ÷ 360 × total. In the pet graph, the cat slice is 108 degrees and the class has 30 students, so 108 ÷ 360 × 30 is 9 students.
How to Draw a Circle Graph by Hand
You need a compass, a protractor, a ruler and your table of angles. The CK-12 text describes the core of the method in three moves: draw a circle with a compass, draw one radius, and use that radius as a side of the first central angle, then measure the others with a protractor. Here it is in full.
- Draw the circle. Set the compass to a radius of about 2 inches (5 cm) and draw the circle. Mark the center point clearly. You will need it for every slice.
- Draw the first radius. Use the ruler to draw a straight line from the center to the top of the circle. This is your starting line.
- Measure the first angle. Arnold’s textbook explains the protractor: set the notch in the middle of its base on the center of the circle, and line up its base with your starting line. Find your first angle on the scale, 144 degrees for the dog slice, and make a small mark at the edge.
- Draw the second radius. Join the center to the mark. The space between the two lines is the first slice.
- Repeat from the new line. Line up the base of the protractor with the line you just drew and measure the next angle, 108 degrees for cats. Arnold’s example does the same: each new angle starts from the side of the one before.
- Let the last slice close itself. After the fourth line, the space left over should measure 12 degrees. If it does, your drawing is accurate. If it is off by a degree or two, that is normal for hand work.
- Label, color and title. Write the category and the percentage on or next to each slice, give each slice its own color, and add a title. If the numbers come from somewhere, add the source.
Tips That Save Time
- Start with the biggest slice at the top and work clockwise in order of size. It is the order most readers expect, and small slices end up together where they are easy to label.
- A slice larger than 180 degrees is awkward on a half-circle protractor. Measure the rest of the circle (360 minus the angle) on the other side of your line.
- Use paper with a printed circle if your compass slips. The angles are what matter, not the circle.
These tips are our own, from drawing the examples in this guide.
How to Read a Circle Graph
Reading one takes four steps.
- Read the title to learn what the whole circle stands for, and how big the whole is if it says.
- Match each slice to its label or to the legend.
- Compare each slice to the easy fractions. Half a circle is 50 percent, a quarter is 25 percent, a square corner at the center is 90 degrees.
- Turn percentages into counts when you need them. Multiply the percentage by the total and divide by 100.
Practice Questions
Use the pet graph above. The answers follow each question.
- Which pet is the most popular, and what share of the class chose it? Dog, with 12 of 30 students, or 40 percent.
- What percentage of the class chose a dog or a cat? 40 plus 30 is 70 percent, which is 21 students.
- The fish slice has a central angle of 60 degrees. What fraction of the class is that? 60 ÷ 360 is one sixth, and one sixth of 30 is 5 students.
- Bird is 10 percent of the class. How many students is that? 10 × 30 ÷ 100 is 3 students.
- How many more students chose a dog than a bird? 12 minus 3 is 9 students.
Pie Chart Examples
Here are three more examples. Each one works as a circle graph for a different reason.
Simple Fractions: A Class Election
Votes for class president. Maya has 16 of 32 votes, exactly half the circle, and the other two candidates have a quarter each. Sample data.
Show the data
| Slice | Value |
|---|---|
| Maya | 16 |
| Leo | 8 |
| Priya | 8 |
You can read this one without any numbers: one half and two quarters. Claus Wilke’s textbook Fundamentals of Data Visualization says pie charts work well when the goal is to emphasize simple fractions such as one half, one third or one quarter. The angles are 180, 90 and 90 degrees.
Parts of a Recipe: Trail Mix
A 250 gram trail mix by ingredient. Peanuts are 100 grams, which is 40 percent of the bag. Sample data.
Show the data
| Slice | Value |
|---|---|
| Peanuts | 100 |
| Raisins | 60 |
| Almonds | 40 |
| Chocolate | 30 |
| Seeds | 20 |
The whole is 250 grams, so each percentage is the grams divided by 250 and multiplied by 100: 40, 24, 16, 12 and 8 percent. The angles are 144, 86.4, 57.6, 43.2 and 28.8 degrees.
Hours in a Day
A student's 24 hours on a school day. Sleep and school together take 15 hours, more than half the circle. Sample data.
Show the data
| Slice | Value |
|---|---|
| Sleep | 8 |
| School | 7 |
| Homework | 2 |
| Meals | 2 |
| Screen time | 2 |
| Sports | 1.5 |
| Other | 1.5 |
A day is a natural whole: the slices must add up to 24 hours. Every hour is 15 degrees, because 360 ÷ 24 is 15. This graph has seven slices, which is about as many as a circle graph can carry. Microsoft’s Excel help gives the same limit: pie charts work best with no more than seven categories, because more slices make a chart hard to read.
When a Bar Graph Is Better
A circle graph answers one question well: how big is this part compared with the whole? It is weaker at a different question: which of these parts is bigger?
Five teams with similar scores. Without labels, it is hard to say which slice is the largest or to put the teams in order. Sample data.
Show the data
| Slice | Value |
|---|---|
| Team A | 22 |
| Team B | 21 |
| Team C | 20 |
| Team D | 19 |
| Team E | 18 |
The values are 22, 21, 20, 19 and 18, and the slices look almost the same. Now the same numbers as bars.
The same five scores as a bar graph. The order from Team A down to Team E is clear at a glance. Sample data.
Show the data
| Category | Points |
|---|---|
| Team A | 22 |
| Team B | 21 |
| Team C | 20 |
| Team D | 19 |
| Team E | 18 |
Stephen Few, a writer on data visualization, explains why in his 2007 essay Save the Pies for Dessert: pie charts encode values as areas and angles, and he argues that our eyes compare positions and lengths much better than areas and angles. Wikipedia’s summary of the research is more balanced. It says comparisons between categories are easier with a bar chart, but that a pie chart can be more effective when the goal is to compare one slice with the whole and that slice is close to 25 or 50 percent.
So here is a fair rule, and the choice is a judgment call, not a law:
- Use a circle graph for a few parts of one whole, especially when one part is near a quarter, a third or a half.
- Use a bar graph when the parts are close in size, when there are many of them, or when the reader needs the exact order. Our bar graph examples show the options, and the bar graph tool draws them.
- Do not use a circle graph for numbers that are not parts of one whole, such as the heights of five students, or when a value is zero or negative. Microsoft’s help page lists both conditions: one data series, and no values that are zero or less.
A circle graph with a hole in the middle is a donut chart. It follows the same arithmetic, and our guide to the donut chart vs the pie chart covers when the hole helps.
Circle Graph Templates to Start From
If you would rather not reach for a protractor, a circle graph template gets you there faster. The gallery below has eight, including a monthly budget, a class survey, election results and a workday. The numbers in them are sample data. Open one and type your own.
Each template opens in our pie chart tool. You type a label and a value on each row, and it works out the percentage of every slice for you. Under “Labels on slices” you choose between the percentage, the value, the label with its percentage, or nothing, and “Decimal places” sets how the percentages are rounded. Rows with a value of zero or less are skipped, with a note telling you which. The tool does not print the angles, so for a hand drawing you still multiply by 3.6.
Open a blank circle graph with four slices
For the other chart families and when each one fits, see our guide to the types of graphs and charts.
Summary
A circle graph is a pie chart: one circle, one whole, one slice per part. To draw it, divide each value by the total, multiply by 100 for the percentage and by 360 for the angle, check that the totals are 100 and 360, then measure each angle from the last line with a protractor. Read it by comparing slices with halves and quarters. When the slices are many or nearly equal, switch to bars.
Questions people ask
What is a circle graph?
A circle graph is a circle cut into slices, where each slice shows one part of a whole. The bigger the part, the wider the slice, and together the slices fill the full circle, which stands for 100 percent. It is the same chart that is more often called a pie chart.
What are the circle graphs called?
The usual name is pie chart. Wikipedia also lists circle chart, and school materials often say circle graph or pie graph. The pieces have names too: each one is a slice, a wedge or, in geometry terms, a sector, and the angle at its tip is the central angle.
How to make a circle graph step by step?
Add up the values to get the total. Divide each value by the total and multiply by 360 to get its angle. Draw a circle with a compass, draw one radius, and measure each angle from the last line with a protractor. Label every slice, then add a title.
What should be included in a pie chart?
The NCES Kids' Zone guide names four parts: a title that says what the chart is about, a legend that tells what each slice stands for, a source that says where the numbers came from, and the data itself. We would add a label on each slice with its percentage or value.
What is a pie chart with examples?
A pie chart shows how one total splits into parts. Typical examples are the votes each candidate received in one election, the ingredients in a recipe by weight, or the hours of one day by activity. In each case the parts add up to a single whole that means something.
What is the circle graph formula?
There are two. The percentage of a slice is its value divided by the total, times 100. The angle of a slice is its value divided by the total, times 360. If you already have the percentage, multiply it by 3.6 to get the degrees, because 360 divided by 100 is 3.6.
Is there a circle graph calculator?
For the percentages, yes: type your labels and values into our pie chart tool and it works out the share of each slice and draws the graph. It does not print the angles. For those, multiply each percentage by 3.6, or divide the value by the total and multiply by 360.
