# Pie Charts (Sector Graphs)

> Read a pie chart as fractions of 360 degrees, find the angle for each slice, turn an angle back into a number, and work with percentage pie charts.

From Selective School Maths on WhizzNotes, free study notes for NSW students: https://whizznotes.com/selective-school-maths/pie-charts/. Updated 4 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: The sports vote
Ninety students at Ridgeview School vote for their favourite sport. Soccer gets 30 votes, netball 20, cricket 25 and tennis 15.

The principal wants to put the results in the newsletter as a pie chart. "How big is the soccer slice?" she asks. Ava works it out: soccer got 30 out of 90, which is a third of the votes. A whole circle is 360 degrees, and a third of 360 is 120. "The soccer slice is 120 degrees," she says.

**In short:** A pie chart is a circle cut into slices called sectors, and the whole circle is 360°. A slice's angle is its fraction of the total times 360°. To go back, the number in a slice is its angle out of 360 times the total.

## Before you start

- A full turn is 360° (see Types of Angles).
- Fractions of a quantity and percentages (see Fractions of a Quantity and Fractions, Decimals and Percentages).

## Slices are fractions of 360°

| Part of the pie | Angle |
|---|---|
| All of it | 360° |
| Half | 180° |
| A quarter | 90° |
| A third | 120° |
| A tenth | 36° |

## Finding the angle for each slice

### Key idea: From a number to an angle
$$\text{angle} = \frac{\text{number in the slice}}{\text{total}} \times 360°$$

### Worked example: The sports vote
Total $= 90$ students.

- Soccer: $\frac{30}{90} \times 360° = 120°$
- Netball: $\frac{20}{90} \times 360° = 80°$
- Cricket: $\frac{25}{90} \times 360° = 100°$
- Tennis: $\frac{15}{90} \times 360° = 60°$

Check: $120 + 80 + 100 + 60 = 360$.

*Diagram: Pie chart of the sports vote: soccer 120 degrees, netball 80 degrees, cricket 100 degrees, tennis 60 degrees*
*The four slices add up to the whole circle, 360°.*

To draw a pie chart, draw a circle and one radius. Put the centre of a protractor on the middle, measure the first angle and draw the next radius. Carry on from that line for each slice.

## From an angle back to a number

### Key idea: From an angle to a number
$$\text{number} = \frac{\text{angle}}{360°} \times \text{total}$$

### Worked example: 300 people
A pie chart shows 300 people. One slice is 72°. $\frac{72}{360} = \frac{1}{5}$, and $\frac{1}{5}$ of 300 is 60 people.

## Percentage pie charts

Some pie charts give percentages. 100% is the whole circle, so **1% is 3.6°**.

- 25% is $\frac{1}{4}$ of 360°, which is 90°.
- 10% is 36°.
- If the slices are 35%, 25% and 15%, the last slice is $100\% - 75\% = 25\%$, which is 90°.

### Watch out: Angles are not the numbers
A 60° slice does not mean 60 people. It means $\frac{60}{360} = \frac{1}{6}$ of everyone.

### Challenge: Selective level: finding the total
In a pie chart, 18 students make a slice of 54°. $\frac{54}{360} = \frac{3}{20}$, so 18 students is $\frac{3}{20}$ of the class. $\frac{1}{20}$ is 6 students, and the whole class is $20 \times 6 = 120$.

A pie chart shows how Ana spends a day. Sleep is a 135° slice. $\frac{135}{360} = \frac{3}{8}$, and $\frac{3}{8}$ of 24 hours is 9 hours.

**Mind map**

```text
Pie charts
  The whole
    360 degrees
    Half is 180
    Quarter is 90
  Angle of a slice
    Fraction of total x 360
    Slices add to 360
  Back to a number
    Angle over 360 x total
  Percentages
    1% is 3.6 degrees
    25% is 90 degrees
```

## Quick summary

- A pie chart is a circle of 360°, cut into sectors.
- Angle of a slice $= \frac{\text{number}}{\text{total}} \times 360°$.
- Number in a slice $= \frac{\text{angle}}{360°} \times \text{total}$.
- All the angles add to 360°, and all the percentages add to 100%.
- In a percentage pie chart, 1% is 3.6°, so 25% is 90°.

## Quiz

Try these questions from the chapter quiz.

1. How many degrees are in a whole pie chart?
   - A. 100°
   - B. 180°
   - C. 360°
   - D. 90°
   - Answer: C. 360°. A full circle is 360°.

2. A slice is half of the pie. What is its angle?
   - A. 90°
   - B. 180°
   - C. 120°
   - D. 360°
   - Answer: B. 180°. Half of 360° is 180°.

3. A slice has an angle of 90°. What fraction of the pie is it?
   - A. $\frac{1}{2}$
   - B. $\frac{1}{3}$
   - C. $\frac{1}{4}$
   - D. $\frac{1}{9}$
   - Answer: C. $\frac{1}{4}$. $\frac{90}{360} = \frac{1}{4}$.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/selective-school-maths/pie-charts/#quiz