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Circle Graph (Pie Chart)

A circle graph, also called a pie chart, is a circular chart that is divided into slices (sectors) to show how a whole is split into parts. The size of each slice represents the proportion of each category compared to the total.

A circle graph is a statistical graphic in which a circle is divided into sectors, where the arc length and area of each sector are proportional to the quantity it represents. The entire circle represents 100% of the data, and each sector's central angle is calculated as the category's fraction of the total multiplied by 360°.

Key Formula

Central Angle=Category ValueTotal×360°\text{Central Angle} = \frac{\text{Category Value}}{\text{Total}} \times 360°
Where:
  • CategoryValueCategory Value = the numerical value for one category
  • TotalTotal = the sum of all category values
  • 360°360° = the total degrees in a circle

Worked Example

Problem: A class of 30 students was asked to pick their favorite fruit. The results were: Apples — 12, Bananas — 9, Oranges — 6, Grapes — 3. Find the central angle for each sector of a circle graph.
Step 1: Confirm the total by adding all values together.
12+9+6+3=3012 + 9 + 6 + 3 = 30
Step 2: Calculate the central angle for Apples.
1230×360°=144°\frac{12}{30} \times 360° = 144°
Step 3: Calculate the central angle for Bananas.
930×360°=108°\frac{9}{30} \times 360° = 108°
Step 4: Calculate the central angles for Oranges and Grapes.
630×360°=72°,330×360°=36°\frac{6}{30} \times 360° = 72°, \quad \frac{3}{30} \times 360° = 36°
Step 5: Check that all angles add up to 360°.
144°+108°+72°+36°=360°  ✓144° + 108° + 72° + 36° = 360° \;\checkmark
Answer: The central angles are: Apples = 144°, Bananas = 108°, Oranges = 72°, and Grapes = 36°.

Visualization

Why It Matters

Circle graphs appear everywhere — in news articles, business reports, survey results, and science presentations — whenever someone wants to show how parts make up a whole. They make it easy to see at a glance which category is largest or smallest. Understanding how to read and construct pie charts is a key data literacy skill you will use well beyond math class.

Common Mistakes

Mistake: Using a pie chart when the parts don't add up to a meaningful whole.
Correction: A circle graph should only be used when the categories together represent 100% of something. If your categories overlap or don't form a complete set, a bar graph is usually a better choice.
Mistake: Converting percentages to angles incorrectly by forgetting to multiply by 360°.
Correction: A category that is 25% of the total does not get a 25° angle — it gets 0.25×360°=90°0.25 \times 360° = 90°. Always multiply the fraction or decimal by 360°.

Related Terms