How to Make Pie Graphs or Circle Graphs
Read,3 minutes
A pie graph, also called a circle graph, shows how a whole is divided into categories. Each slice represents a fraction of the total.
Core Formulas
- Percent of circle: \(\frac{\text{part}}{\text{whole}}\times 100\%\).
- Central angle: \(\frac{\text{part}}{\text{whole}}\times 360^\circ\).
- Count from percent: \(\text{percent}\times \text{total}\).
Worked Example
If \(18\) of \(60\) students chose soccer, the slice is \(18/60=30\%\), and its central angle is \(0.30(360^\circ)=108^\circ\).
Video Lesson
Original Practice Figures
These saved figures are kept with the lesson for continuity. The exercise text below gives all needed values.
How to Make Pie Graphs or Circle Graphs
Think of this lesson as more than a rule to memorize. The Pie Graph or Circle Graph is about organizing data and choosing the right summary measure. A strong student does not rush to the first formula on the page; they pause, identify the structure of the problem, and then choose the tool that matches that structure. That pause is what prevents most mistakes.
Statistics is about describing data clearly. First organize the values, then choose the measure or graph that best answers the question being asked.
Here is the teacher way to approach the topic. First, read the problem slowly and underline the information that is actually given. Next, name the target: are you finding a value, simplifying an expression, comparing two quantities, solving for a variable, or interpreting a graph? Once the target is clear, the calculation becomes much less mysterious because every step has a job.
- Read the scale and labels first.
- Identify the key values the graph shows.
- Connect the graph to the formula or data table.
- Answer using the units and context.
A helpful habit is to say what each number represents before using it. For example, if a number is a denominator, a radius, a slope, a common difference, or a coefficient, it should not be treated like an ordinary loose number. Its role tells you where it belongs in the formula. This is especially important on ACT-style questions because many wrong answer choices come from using the right numbers in the wrong places.
Another good habit is to keep the work organized vertically. Write one clean line for substitution, one line for simplifying, and one line for the final answer. If the problem has units, keep the units attached. If the problem has signs, exponents, or parentheses, copy them carefully from one line to the next. Most errors in this topic are not caused by a hard idea; they are caused by dropping a negative sign, combining unlike terms, using the wrong denominator, or skipping a check.
When you finish, ask a quick reasonableness question. Should the answer be positive or negative? Should it be larger or smaller than the original number? Does it fit the graph, table, shape, or equation? Can you plug it back into the original problem? This final check turns the lesson from a procedure into understanding.
On a test, the goal is not to write the longest solution. The goal is to write enough clear work that you can see the structure, avoid traps, and recover quickly if one line goes wrong. Practice the examples below with that mindset: identify the type of problem, choose the matching rule, show the substitution, simplify carefully, and check the answer before moving on.
Exercises
Solve each ACT-style practice problem. The questions increase in difficulty.
1) In a circle graph, 12 of 40 students chose art. What percent of the circle is this, and what is the central angle?
2) In a circle graph, 18 of 60 survey responses were yes. What percent of the circle is this, and what is the central angle?
3) In a circle graph, 45 of 150 tickets sold were child tickets. What percent of the circle is this, and what is the central angle?
4) In a circle graph, 24 of 80 books were mysteries. What percent of the circle is this, and what is the central angle?
5) In a circle graph, 72 of 240 votes went to Candidate A. What percent of the circle is this, and what is the central angle?
6) In a circle graph, 33 of 110 members chose basketball. What percent of the circle is this, and what is the central angle?
7) In a circle graph, 125 of 500 downloads were podcasts. What percent of the circle is this, and what is the central angle?
8) In a circle graph, 96 of 320 orders were pickup orders. What percent of the circle is this, and what is the central angle?
9) In a circle graph, 27 of 90 garden plots had tomatoes. What percent of the circle is this, and what is the central angle?
10) In a circle graph, 54 of 180 club dues went to supplies. What percent of the circle is this, and what is the central angle?
11) In a circle graph, 84 of 210 students chose bus transportation. What percent of the circle is this, and what is the central angle?
12) In a circle graph, 78 of 260 surveyed adults preferred tea. What percent of the circle is this, and what is the central angle?
13) In a circle graph, 900 of 2400 budget dollars were spent on rent. What percent of the circle is this, and what is the central angle?
14) In a circle graph, 132 of 330 participants selected morning sessions. What percent of the circle is this, and what is the central angle?
15) In a circle graph, 420 of 1200 streaming minutes were comedies. What percent of the circle is this, and what is the central angle?
16) In a circle graph, 165 of 550 shirts sold were medium. What percent of the circle is this, and what is the central angle?
17) In a circle graph, 48 of 160 volunteers chose cleanup duty. What percent of the circle is this, and what is the central angle?
18) A circle graph for 500 total students has a \(72^\circ\) slice. How many students does that slice represent?
19) A circle graph for 800 total voters has a \(126^\circ\) slice. How many voters does that slice represent?
20) A circle graph for 1200 total sales has a \(54^\circ\) slice. How many sales does that slice represent?
1) Write the fraction of the whole: \(\frac{12}{40}\).
Percent: \(\frac{12}{40}\times 100\%=30\%\).
Angle: \(\frac{12}{40}\times 360^\circ=108^\circ\).
2) Write the fraction of the whole: \(\frac{18}{60}\).
Percent: \(\frac{18}{60}\times 100\%=30\%\).
Angle: \(\frac{18}{60}\times 360^\circ=108^\circ\).
3) Write the fraction of the whole: \(\frac{45}{150}\).
Percent: \(\frac{45}{150}\times 100\%=30\%\).
Angle: \(\frac{45}{150}\times 360^\circ=108^\circ\).
4) Write the fraction of the whole: \(\frac{24}{80}\).
Percent: \(\frac{24}{80}\times 100\%=30\%\).
Angle: \(\frac{24}{80}\times 360^\circ=108^\circ\).
5) Write the fraction of the whole: \(\frac{72}{240}\).
Percent: \(\frac{72}{240}\times 100\%=30\%\).
Angle: \(\frac{72}{240}\times 360^\circ=108^\circ\).
6) Write the fraction of the whole: \(\frac{33}{110}\).
Percent: \(\frac{33}{110}\times 100\%=30\%\).
Angle: \(\frac{33}{110}\times 360^\circ=108^\circ\).
7) Write the fraction of the whole: \(\frac{125}{500}\).
Percent: \(\frac{125}{500}\times 100\%=25\%\).
Angle: \(\frac{125}{500}\times 360^\circ=90^\circ\).
8) Write the fraction of the whole: \(\frac{96}{320}\).
Percent: \(\frac{96}{320}\times 100\%=30\%\).
Angle: \(\frac{96}{320}\times 360^\circ=108^\circ\).
9) Write the fraction of the whole: \(\frac{27}{90}\).
Percent: \(\frac{27}{90}\times 100\%=30\%\).
Angle: \(\frac{27}{90}\times 360^\circ=108^\circ\).
10) Write the fraction of the whole: \(\frac{54}{180}\).
Percent: \(\frac{54}{180}\times 100\%=30\%\).
Angle: \(\frac{54}{180}\times 360^\circ=108^\circ\).
11) Write the fraction of the whole: \(\frac{84}{210}\).
Percent: \(\frac{84}{210}\times 100\%=40\%\).
Angle: \(\frac{84}{210}\times 360^\circ=144^\circ\).
12) Write the fraction of the whole: \(\frac{78}{260}\).
Percent: \(\frac{78}{260}\times 100\%=30\%\).
Angle: \(\frac{78}{260}\times 360^\circ=108^\circ\).
13) Write the fraction of the whole: \(\frac{900}{2400}\).
Percent: \(\frac{900}{2400}\times 100\%=\frac{75}{2}\%\).
Angle: \(\frac{900}{2400}\times 360^\circ=135^\circ\).
14) Write the fraction of the whole: \(\frac{132}{330}\).
Percent: \(\frac{132}{330}\times 100\%=40\%\).
Angle: \(\frac{132}{330}\times 360^\circ=144^\circ\).
15) Write the fraction of the whole: \(\frac{420}{1200}\).
Percent: \(\frac{420}{1200}\times 100\%=35\%\).
Angle: \(\frac{420}{1200}\times 360^\circ=126^\circ\).
16) Write the fraction of the whole: \(\frac{165}{550}\).
Percent: \(\frac{165}{550}\times 100\%=30\%\).
Angle: \(\frac{165}{550}\times 360^\circ=108^\circ\).
17) Write the fraction of the whole: \(\frac{48}{160}\).
Percent: \(\frac{48}{160}\times 100\%=30\%\).
Angle: \(\frac{48}{160}\times 360^\circ=108^\circ\).
18) The slice fraction is \(\frac{72}{360}\).
Percent: \(\frac{72}{360}\times100\%=20\%\).
Count: \(\frac{72}{360}\times 500=100\).
19) The slice fraction is \(\frac{126}{360}\).
Percent: \(\frac{126}{360}\times100\%=35\%\).
Count: \(\frac{126}{360}\times 800=280\).
20) The slice fraction is \(\frac{54}{360}\).
Percent: \(\frac{54}{360}\times100\%=15\%\).
Count: \(\frac{54}{360}\times 1200=180\).
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