Skill: Construct circle graphs

A circle graph shows each category as a sector, or “slice,” of one circle. The size of each slice depends on the category’s share of the total.

Use this formula:

$$\text{central angle}=\frac{\text{category count}}{\text{total count}}\times 360^\circ$$

Example: A class surveys 20 students about their favorite fruit.

Fruit	Number of students
Apples	8
Bananas	6
Oranges	4
Grapes	2

1. Find the total

The total is already given as 20. You can check it:

$$8+6+4+2=20$$

2. Find the angle for each category

For apples:

$$\frac{8}{20}\times 360^\circ=144^\circ$$

For bananas:

$$\frac{6}{20}\times 360^\circ=108^\circ$$

For oranges:

$$\frac{4}{20}\times 360^\circ=72^\circ$$

For grapes:

$$\frac{2}{20}\times 360^\circ=36^\circ$$

Your angle table is:

Fruit	Angle
Apples	$(144^\circ)$
Bananas	$(108^\circ)$
Oranges	$(72^\circ)$
Grapes	$(36^\circ)$

3. Draw and label the circle

1. Use a compass or a circular template to draw one circle.
2. Draw a radius from the center to the edge.
3. Use a protractor to measure $(144^\circ)$ from that radius. Label the sector Apples.
4. From the new radius, measure $(108^\circ)$. Label the next sector Bananas.
5. Measure $(72^\circ)$ for Oranges.
6. The remaining sector should be $(36^\circ)$. Label it Grapes.
7. Add a key or label each sector clearly.

4. Check your work

All sectors must make one full circle:

$$144^\circ+108^\circ+72^\circ+36^\circ=360^\circ$$

Since the angles total $(360^\circ)$, the circle graph is complete.