Pie Charts (Grade 5)
A pie chart (also called a circle graph) is a circular diagram divided into slices. Each slice represents a part of the whole. The bigger the slice, the larger the share of that category.
In Class 5, you learn to read and interpret pie charts where data is given as fractions or percentages. Pie charts are useful when you want to show how a total is divided among different groups.
For example, a pie chart can show how Ria spends her pocket money — what fraction goes to books, food, savings, and games.
What is Pie Charts - Class 5 Maths (Data Handling)?
A pie chart is a circular graph that shows data as parts of a whole. The entire circle represents 100% (or the total amount), and each slice represents a fraction or percentage of that total.
Key facts:
- A full circle = 360°
- All slices together = 100% of the data
- Each slice angle = (value ÷ total) × 360°
Pie Charts (Grade 5) Formula
Angle of a slice = (Value ÷ Total) × 360°
Value of a slice = (Percentage ÷ 100) × Total
Solved Examples
Example 1: Example 1: Reading a Pie Chart
Problem: A pie chart shows how 40 students travel to school: Bus = 50%, Auto = 25%, Walk = 15%, Cycle = 10%. How many students take the bus?
Solution:
Step 1: Bus = 50% of 40
Step 2: (50 ÷ 100) × 40 = 20
Answer: 20 students take the bus.
Example 2: Example 2: Finding a Percentage
Problem: In a class of 50 students, 15 like cricket, 20 like football, 10 like badminton, and 5 like kabaddi. What percentage likes football?
Solution:
Step 1: Percentage = (20 ÷ 50) × 100 = 40%
Answer: 40% of students like football.
Example 3: Example 3: Finding the Angle
Problem: In the above data, find the angle for cricket in the pie chart.
Solution:
Step 1: Cricket = 15 out of 50
Step 2: Angle = (15 ÷ 50) × 360° = 108°
Answer: Cricket slice = 108°
Example 4: Example 4: Budget Problem
Problem: Priya's monthly pocket money is ₹500. The pie chart shows: Books = 30%, Food = 25%, Savings = 20%, Games = 15%, Charity = 10%. How much does she spend on books?
Solution:
Step 1: Books = 30% of ₹500
Step 2: (30 ÷ 100) × 500 = ₹150
Answer: Priya spends ₹150 on books.
Example 5: Example 5: Missing Percentage
Problem: A pie chart shows: Maths = 25%, Science = 30%, English = 20%, Hindi = ?%. Find the percentage for Hindi.
Solution:
Step 1: Total must be 100%
Step 2: Hindi = 100% − 25% − 30% − 20% = 25%
Answer: Hindi = 25%
Example 6: Example 6: All Angles in a Pie Chart
Problem: Calculate the angles for a pie chart showing: Red = 40%, Blue = 30%, Green = 20%, Yellow = 10%.
Solution:
Red = (40/100) × 360° = 144°
Blue = (30/100) × 360° = 108°
Green = (20/100) × 360° = 72°
Yellow = (10/100) × 360° = 36°
Check: 144 + 108 + 72 + 36 = 360° ✓
Answer: Red = 144°, Blue = 108°, Green = 72°, Yellow = 36°
Example 7: Example 7: Fraction to Pie Chart
Problem: A pie chart shows how Aman spends 24 hours: Sleep = 1/3, School = 1/4, Play = 1/6, Study = 1/8, Other = rest. Find the hours for each.
Solution:
Sleep = 1/3 × 24 = 8 hours
School = 1/4 × 24 = 6 hours
Play = 1/6 × 24 = 4 hours
Study = 1/8 × 24 = 3 hours
Other = 24 − 8 − 6 − 4 − 3 = 3 hours
Answer: Sleep = 8 h, School = 6 h, Play = 4 h, Study = 3 h, Other = 3 h
Example 8: Example 8: Comparing Slices
Problem: A pie chart shows sales: Product A = 35%, Product B = 25%, Product C = 40%. Total sales = ₹2,00,000. Which product earned the most and how much?
Solution:
Step 1: Product C has the largest percentage: 40%.
Step 2: Product C sales = (40/100) × 2,00,000 = ₹80,000
Answer: Product C earned the most: ₹80,000.
Example 9: Example 9: From Angle to Value
Problem: In a pie chart, the "Sports" slice has an angle of 90°. The total number of students is 200. How many students chose sports?
Solution:
Step 1: Fraction of circle = 90° ÷ 360° = 1/4
Step 2: Students = 1/4 × 200 = 50
Answer: 50 students chose sports.
Key Points to Remember
- A pie chart is a circle divided into slices representing parts of a whole.
- The full circle = 360° = 100%.
- Angle of slice = (value ÷ total) × 360°.
- All percentages in a pie chart must add up to 100%.
- All angles must add up to 360°.
- Larger slice = larger share of the total.
- Pie charts are best when showing how parts make up a whole.
Practice Problems
- A pie chart shows how 60 students chose activities: Dance = 30%, Singing = 25%, Painting = 20%, Drama = 25%. How many students chose painting?
- Calculate the angle for a slice representing 45% in a pie chart.
- In a pie chart, three slices show 120°, 90°, and 60°. What is the angle of the fourth slice?
- Kavi's monthly expenses total ₹10,000. Rent = 40%, Food = 30%, Transport = 15%, Savings = 15%. How much is spent on food?
- A pie chart slice has an angle of 72°. What percentage of the total does it represent?
- Draw a rough pie chart for: Water = 50%, Land = 30%, Ice = 20%.
- If 25% of 800 students like Maths, how many students is that? What angle would the Maths slice have?
Frequently Asked Questions
Q1. What is a pie chart?
A pie chart is a circular graph divided into slices. Each slice represents a portion of the total. The whole circle equals 100% or 360°.
Q2. When should you use a pie chart instead of a bar graph?
Use a pie chart when you want to show how parts make up a whole (like budget distribution). Use a bar graph when you want to compare individual values across categories.
Q3. How do you calculate the angle for a pie chart slice?
Angle = (value ÷ total) × 360°. For example, if 20 out of 80 students chose cricket, the angle = (20/80) × 360° = 90°.
Q4. What should all the percentages in a pie chart add up to?
All percentages must add up to exactly 100%. If they do not, there is an error in the data.
Q5. Can a pie chart show more than 5 or 6 categories?
Technically yes, but too many slices make the chart hard to read. If there are many small categories, they are often grouped under 'Others'.
Q6. How do you read the value of a slice if only the percentage is given?
Multiply: Value = (percentage ÷ 100) × total. For example, 25% of 400 = (25/100) × 400 = 100.
Q7. What does a half circle (180°) represent in a pie chart?
A half circle represents exactly 50% of the total — half the data belongs to that category.
Q8. Can a pie chart have equal slices?
Yes. If all categories have the same value, all slices will be equal. For 4 equal categories, each slice = 360° ÷ 4 = 90°.
