Circle Graph
A circle graph (pie chart) shows how a whole is divided into parts, with each sector representing a category. In Grade 6 Saxon Math Course 1 (Chapter 5: Number and Operations), the central angle of each sector equals the category fraction multiplied by 360°. If 1/4 of a class prefers soccer, the sector angle = (1/4) × 360° = 90°. Students read circle graphs to find what fraction or percent each sector represents and construct them by calculating sector angles. Circle graphs are most useful when showing parts of a whole rather than change over time.
Key Concepts
Property In a circle graph, each category corresponds to a sector of the circle. The number of degrees in a fraction of a circle is the fraction times $360^\circ$.
Examples To find the angle for a category representing $\frac{3}{12}$ of the data: $\frac{3}{12} \times 360^\circ = 90^\circ$. To find the angle for a category representing $\frac{5}{12}$ of the data: $\frac{5}{12} \times 360^\circ = 150^\circ$. If 25% of students prefer blue, their sector angle is $0.25 \times 360^\circ = 90^\circ$.
Explanation Think of a pizza! A circle graph, or pie chart, shows parts of a whole, just like slices of a pizza. To figure out how big each slice (sector) should be, you turn its fraction into an angle. Since a full circle is $360^\circ$, a category that's $\frac{1}{4}$ of the total gets a $90^\circ$ slice.
Common Questions
How do you calculate the angle of a sector in a circle graph?
Multiply the fraction representing the category by 360°. For example, if 2/5 of students prefer math, the sector angle = 2/5 × 360° = 144°.
Why does a full circle equal 360 degrees?
A full rotation is defined as 360°. Since a circle graph represents one complete whole, all sector angles must add up to 360°.
If a circle graph has a sector of 90°, what fraction of the whole does it represent?
90° ÷ 360° = 1/4. The sector represents one quarter of the total.
How do you read a circle graph?
Identify each sector label and its corresponding angle or percent. The larger the sector, the greater the portion of the whole it represents.
When is a circle graph the best choice for displaying data?
When showing how parts make up a whole, such as budget categories or survey responses. It is not ideal for showing changes over time, which a line graph handles better.