Pie Chart Practice Questions Practice Test Worksheets
Pie chart questions follow a small set of predictable patterns. Once you know them, they become one of the most reliable marks on any test. This page walks you through the key methods with worked examples.
For students who understand fractions of a circle, but lose marks converting pie-chart sectors into values and angles.
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What Do Pie Chart Questions Look Like?
Pie chart questions test your ability to convert between angles, fractions, percentages, and real counts. The example below uses one complete survey chart with three linked questions, just like the practice papers.
A Survey of Favourite Music
Question: The pie chart below represents data collected in a survey about the favourite types of music of a sample of school children.
(a) Calculate the angle of the sector for classical.
(b) 100 children chose rock as their favourite type of music. Calculate the total number of children who took part in the survey.
(c) What percentage of school children chose R&B as their favourite type of music? Give your answer to 1 decimal place.
Worked Method
(a) Find the missing angle
A full circle is 360°. First add the four given angles.
125° + 50° + 50° + 80° = 305°
Classical angle = 360° − 305° = 55°
(b) Find the survey total
Rock represents 50° of the circle, and 100 children chose Rock.
Fraction choosing Rock = 50360
Total = 100 ÷ 50360
= 100 × 36050
= 720 children
(c) Find the R&B percentage
R&B represents 80° of the circle.
Percentage = 80360 × 100
= 22.222…%
To 1 decimal place: 22.2%
Tip: Use 360° for the whole circle. To find the total from one sector, multiply its count by 360 and divide by its angle.
Rules to Help You Solve Pie Chart Questions
Almost every pie chart question tests one (or more) of these four ideas. Understanding them before you practise makes everything click faster:
🔵 Rule 1: A full circle = 360°
All sectors must add up to exactly 360°. If you're given four sectors and one is missing, simply subtract the rest from 360.
Example: Sectors of 90°, 120°, 75° → missing sector = 360 − 90 − 120 − 75 = 75°
🟠 Rule 2: Angle → Fraction → Amount
A sector angle represents a fraction of the whole group. Write the angle over 360, simplify if you can, then multiply by the total.
Example: 90° sector, 200 people total → 90360 = 14 → 14 × 200 = 50 people
🟢 Rule 3: Working backwards to find the total
If you know how many people are in one sector and its angle, you can reverse-calculate the total. Divide the count by the fraction.
Example: 50° sector = 100 people → 50360 = 536 → total = 100 ÷ 5 × 36 = 720
🔴 Rule 4: Angle → Percentage
To convert a sector to a percentage, divide the angle by 360 and multiply by 100. Follow the question's rounding instructions.
Example: 80° sector → 80360 × 100 ≈ 22.2% to 1 decimal place.
Two More Worked Examples
Practise finding survey totals, sector counts, fractions and percentages. Each chart has three linked questions from the practice papers.
A Survey of Favourite Hobbies
Question: The pie chart below represents data collected in a survey about the favourite hobbies of a sample of school children.
(a) Calculate the angle of the sector for reading.
(b) 84 children chose dancing as their favourite hobby. Calculate the total number of children who took part in the survey.
(c) Using your answer from part (b), calculate how many children chose art as their favourite hobby.
Worked Method
(a) Find the missing angle
Add the three given angles.
75° + 130° + 70° = 275°
Reading angle = 360° − 275° = 85°
(b) Find the survey total
Dancing represents 70° of the circle, and 84 children chose Dancing.
Fraction choosing Dancing = 70360
Total = 84 ÷ 70360
= 84 × 36070
= 432 children
(c) Find the number who chose Art
Use the total of 432 children from part (b). Art represents 75°.
Number choosing Art = 75360 × 432
= 524 × 432
= 90 children
Tip: Find the whole survey total before calculating the number in another sector.
A Survey of Favourite Pets
Question: The pie chart below represents data collected in a survey about the favourite pets of a sample of school children.
(a) What fraction of the children chose bird as their favourite pet? Give your answer in its lowest form.
(b) Calculate the angle of the sector for rabbit. Express this angle as a fraction of 360°, giving your answer in its lowest form.
(c) What percentage of school children chose hamster as their favourite pet? Give your answer to 1 decimal place.
Worked Method
(a) Find the fraction who chose Bird
Bird represents 55° of the circle.
Fraction choosing Bird = 55360
Divide the numerator and denominator by 5.
In lowest form: 1172
(b) Find the Rabbit angle and fraction
Add the four given angles.
85° + 65° + 55° + 110° = 315°
Rabbit angle = 360° − 315° = 45°
Fraction of the circle = 45360
Divide the numerator and denominator by 45.
In lowest form: 18
(c) Find the Hamster percentage
Hamster represents 65° of the circle.
Percentage = 65360 × 100
= 18.055…%
To 1 decimal place: 18.1%
Tip: Simplify fractions fully and round percentages only at the final step.
