A pie chart is a circle divided into sectors, where each sector's angle is directly proportional to the frequency it represents. Because a full circle is $360°$, every calculation reduces to one relationship:

Every sector angle you calculate should sum to exactly $360°$ — this is a free, built-in check on your working.

Example: 30 people chose a favourite colour; 11 chose red.

Find the unit rate — how many items one degree represents — then scale it to whatever's needed.

Example: a $30°$ sector represents 15 people. One degree represents $15 \div 30 = 0.5$ people. The total frequency is therefore $0.5 \times 360 = 180$ people.

This label is a direct instruction: do not measure angles with a protractor. You must reason using ratio and proportion instead, comparing the given sector to $360°$.

Example: a $90°$ sector (not to scale) represents \12{,}000$. Since$360°$is four times$90°, the total must be four times \12,000, giving \48{,}000$.

A pie chart (not to scale) shows how 180 students travel to school. The "Bus" sector has an angle of $80°$. Find the number of students who travel by bus, and the angle for "Walk" if 63 students walk.

1. Unit rate: $\dfrac{360°}{180} = 2°$ per student, so 1 student $= 2°$, meaning 1° represents $0.5$ students.
2. Bus students: $80° \div 2° = 40$ students.
3. Walk angle: $63 \times 2° = 126°$.

Answer: 40 students travel by bus; the "Walk" sector has an angle of $126°$.

A pie chart shows how parts contribute to a whole, making it ideal for proportions, but it becomes cluttered beyond about 5–6 categories and cannot show negative values. A bar chart handles many categories cleanly and makes it far easier to compare two similar-sized categories directly, since judging small differences between sector angles by eye is notoriously unreliable.