Pie Chart
A pie chart (also called a circle graph) is a circular diagram divided into sectors that represent different parts of a whole. Each sector shows the proportion of a category relative to the total.
Pie charts are widely used to display data like monthly expenditure, marks distribution, population distribution, and survey results. The entire circle represents 100% (or the total), and each sector represents a percentage of that total.
Unlike bar graphs (which compare values across categories) or line graphs (which show trends over time), pie charts are specifically designed to show how a total is divided into parts. They give an immediate visual impression of which categories are largest and smallest.
For example, if a family spends Rs 20,000 per month, a pie chart can instantly show that the largest portion goes to rent, the second largest to food, and so on. The size of each slice tells you the relative importance of each category.
In Class 8, you will learn how to read and interpret pie charts, calculate the central angle for each sector using the formula (Value/Total) × 360°, convert between angles, percentages, and actual values, and draw accurate pie charts using a compass and protractor.
What is Pie Chart?
Definition: A pie chart is a circular statistical graph divided into slices (sectors) to show the relative sizes of data categories.
The key formula for calculating the central angle of each sector:
Central Angle = (Value / Total) × 360°
Where:
- Value = the data value of a particular category
- Total = the sum of all data values
- 360° = the total angle in a circle
To convert to percentage:
Percentage = (Value / Total) × 100%
Methods
Steps to draw a pie chart:
- Collect the data and find the total of all values.
- Calculate the central angle for each category: (Value/Total) × 360°.
- Verify that the sum of all central angles = 360°. If it does not add up due to rounding, adjust the largest sector.
- Draw a circle of suitable size using a compass.
- Draw a radius (a line from the centre to the edge) as the starting line. This is usually drawn pointing upward (12 o'clock position).
- Using a protractor, measure the first sector angle from the starting line and draw a new radius.
- From the new radius, measure the second sector angle and draw another radius. Continue until all sectors are drawn.
- Shade or colour each sector differently for visual distinction.
- Label each sector with the category name, value, and/or percentage.
- Add a title and a legend (colour key) if colours are used.
Steps to read (interpret) a pie chart:
- Read the title to understand what data the pie chart represents.
- Identify which sector is the largest (highest proportion) and smallest (lowest proportion).
- Read the percentage or angle of each sector from the labels.
- To find the actual value: Value = (Angle / 360°) × Total.
- To find the percentage: Percentage = (Angle / 360°) × 100%.
- To compare two sectors: compare their angles or percentages directly.
Important points:
- The sum of all sector angles must be exactly 360°.
- The sum of all percentages must be exactly 100%.
- A pie chart is best used when you have 4 to 8 categories. Too many slices make it hard to read.
- Pie charts show parts of a whole — they do not show changes over time (use line/bar graphs for that).
- When two sectors have similar sizes, it can be hard to tell which is larger. In such cases, always check the exact angle or percentage.
- Pie charts should NOT be used when categories do not add up to a meaningful total.
Solved Examples
Example 1: Example 1: Calculating central angles
Problem: A student scores the following marks: Maths 90, Science 70, English 60, Hindi 50, Social Science 30. Draw a pie chart by finding the central angle for each subject.
Solution:
Total marks: 90 + 70 + 60 + 50 + 30 = 300
Central angles:
- Maths = (90/300) × 360° = 108°
- Science = (70/300) × 360° = 84°
- English = (60/300) × 360° = 72°
- Hindi = (50/300) × 360° = 60°
- Social Science = (30/300) × 360° = 36°
Verification: 108° + 84° + 72° + 60° + 36° = 360° ✓
Answer: The central angles are 108°, 84°, 72°, 60°, and 36° respectively.
Example 2: Example 2: Reading a pie chart
Problem: A pie chart shows monthly expenditure of Rs 18,000. The sector for Food has a central angle of 120°. Find the amount spent on Food.
Solution:
Given:
- Total expenditure = Rs 18,000
- Angle for Food = 120°
Using formula:
- Amount = (Angle / 360°) × Total
- Amount = (120/360) × 18,000
- Amount = (1/3) × 18,000 = Rs 6,000
Answer: Amount spent on Food = Rs 6,000.
Example 3: Example 3: Finding percentage from angle
Problem: In a pie chart, the sector for Transport has an angle of 54°. What percentage does Transport represent?
Solution:
Given: Angle = 54°
Using formula:
- Percentage = (Angle / 360°) × 100%
- Percentage = (54/360) × 100%
- Percentage = 0.15 × 100% = 15%
Answer: Transport represents 15% of the total.
Example 4: Example 4: Finding angle from percentage
Problem: In a survey, 35% of students prefer Cricket. What is the central angle for Cricket in a pie chart?
Solution:
Given: Percentage = 35%
Using formula:
- Angle = (Percentage / 100) × 360°
- Angle = (35/100) × 360°
- Angle = 0.35 × 360° = 126°
Answer: Central angle for Cricket = 126°.
Example 5: Example 5: Monthly budget pie chart
Problem: A family budget of Rs 40,000 is divided as: Rent Rs 12,000, Food Rs 10,000, Education Rs 8,000, Savings Rs 6,000, Others Rs 4,000. Find the central angles.
Solution:
Total: Rs 40,000
Central angles:
- Rent = (12,000/40,000) × 360° = 108°
- Food = (10,000/40,000) × 360° = 90°
- Education = (8,000/40,000) × 360° = 72°
- Savings = (6,000/40,000) × 360° = 54°
- Others = (4,000/40,000) × 360° = 36°
Verification: 108° + 90° + 72° + 54° + 36° = 360° ✓
Answer: The central angles are 108°, 90°, 72°, 54°, 36°.
Example 6: Example 6: Finding unknown value
Problem: A pie chart has 4 sectors with angles 100°, 80°, 70°, and x°. Find x.
Solution:
Given: Sum of all angles = 360°
Calculating:
- 100° + 80° + 70° + x° = 360°
- 250° + x° = 360°
- x° = 360° − 250° = 110°
Answer: x = 110°.
Example 7: Example 7: Comparing sectors
Problem: In a pie chart of total sales = Rs 72,000, sector A has angle 100° and sector B has angle 60°. Which sector has more sales and by how much?
Solution:
Sales for each:
- Sector A = (100/360) × 72,000 = Rs 20,000
- Sector B = (60/360) × 72,000 = Rs 12,000
Difference:
- 20,000 − 12,000 = Rs 8,000
Answer: Sector A has more sales by Rs 8,000.
Example 8: Example 8: Students in different sports
Problem: In a school of 600 students: Cricket 200, Football 150, Badminton 100, Tennis 80, Others 70. Find the central angles for a pie chart.
Solution:
Total: 600 students
Central angles:
- Cricket = (200/600) × 360° = 120°
- Football = (150/600) × 360° = 90°
- Badminton = (100/600) × 360° = 60°
- Tennis = (80/600) × 360° = 48°
- Others = (70/600) × 360° = 42°
Verification: 120° + 90° + 60° + 48° + 42° = 360° ✓
Answer: Central angles are 120°, 90°, 60°, 48°, 42°.
Example 9: Example 9: Finding total from pie chart
Problem: In a pie chart, the sector for Mathematics has an angle of 72° and represents 40 students. Find the total number of students.
Solution:
Given:
- Angle for Maths = 72°
- Students in Maths = 40
Using formula:
- Value = (Angle/360°) × Total
- 40 = (72/360) × Total
- 40 = (1/5) × Total
- Total = 40 × 5 = 200
Answer: Total number of students = 200.
Example 10: Example 10: Fractional data
Problem: In a class, 1/4 of students like Maths, 1/3 like Science, 1/6 like English, and the rest like Hindi. Find the central angle for each in a pie chart.
Solution:
Finding the fraction for Hindi:
- Maths + Science + English = 1/4 + 1/3 + 1/6
- LCM of 4, 3, 6 = 12
- = 3/12 + 4/12 + 2/12 = 9/12 = 3/4
- Hindi = 1 − 3/4 = 1/4
Central angles:
- Maths = (1/4) × 360° = 90°
- Science = (1/3) × 360° = 120°
- English = (1/6) × 360° = 60°
- Hindi = (1/4) × 360° = 90°
Verification: 90° + 120° + 60° + 90° = 360° ✓
Answer: Maths = 90°, Science = 120°, English = 60°, Hindi = 90°.
Real-World Applications
Real-world applications of pie charts:
- Budget and expenditure: Showing how a household or company divides its budget across categories like rent, food, transport, and savings.
- Survey results: Displaying preferences — favourite subjects, sports, food choices — in polls and surveys.
- Business: Showing market share of different companies or products.
- Population data: Displaying religion-wise, age-wise, or region-wise distribution of a population.
- Marks analysis: Showing how marks are distributed across different subjects.
- Time management: Displaying how a student spends 24 hours — study, sleep, play, meals, etc.
- Election results: Showing the vote share of different parties or candidates.
Key Points to Remember
- A pie chart is a circular graph divided into sectors, each representing a part of the whole.
- The entire circle = 360° = 100% of the data.
- Central angle = (Value / Total) × 360°.
- Percentage = (Value / Total) × 100%.
- The sum of all sector angles must be 360°.
- 1% of the circle = 3.6°.
- To draw a pie chart, you need a compass (to draw the circle) and a protractor (to measure angles).
- Pie charts are best for showing parts of a whole, not for comparing trends over time.
- Use 4–8 categories for a clear pie chart. Too many slices make it unreadable.
- Always label each sector with the category name and percentage.
Practice Problems
- A student spends 6 hours sleeping, 8 hours in school, 3 hours studying, 2 hours playing, and 5 hours on other activities. Find the central angle for each and draw a pie chart.
- A pie chart shows the favourite fruit of 200 students. The sector for Mango has an angle of 90°. How many students prefer Mango?
- In a pie chart, sectors have angles 110°, 95°, 80°, and x°. Find x.
- Convert these percentages to central angles: 40%, 25%, 20%, 15%.
- A company's revenue of Rs 5,00,000 is divided as: Product A Rs 2,00,000, Product B Rs 1,50,000, Product C Rs 1,00,000, Product D Rs 50,000. Calculate the central angles.
- The sector for Rent in a pie chart has an angle of 144°. What percentage of the total budget is spent on Rent?
- In a pie chart, the sector for Cricket is 108° and represents 150 students. Find the total number of students surveyed.
- Draw a pie chart for: India's land use — Agricultural 55%, Forest 22%, Wasteland 13%, Other 10%.
Frequently Asked Questions
Q1. What is a pie chart?
A pie chart is a circular graph divided into sectors (slices) that represent different categories of data. The entire circle represents the total (100%), and each sector shows its share.
Q2. How do you calculate the angle for a pie chart?
Central Angle = (Value / Total) × 360°. For example, if a category has value 30 out of total 120, its angle = (30/120) × 360° = 90°.
Q3. What tools are needed to draw a pie chart?
A compass to draw the circle, a protractor to measure and mark the sector angles, a ruler to draw radii, and coloured pencils or markers to shade each sector.
Q4. What is the total angle in a pie chart?
The total angle is always 360° because a pie chart is a complete circle. The sum of all sector angles must equal 360°.
Q5. How is a pie chart different from a bar graph?
A pie chart shows parts of a whole (proportions), while a bar graph compares quantities across categories. Pie charts use sectors; bar graphs use rectangular bars.
Q6. How many degrees represent 1%?
1% of a pie chart = 360° / 100 = 3.6°. So 10% = 36°, 25% = 90°, 50% = 180°.
Q7. Can a pie chart have more than 360°?
No. A pie chart always totals exactly 360° because it represents a complete circle. If your angles add up to more or less than 360°, there is a calculation error.
Q8. When should you NOT use a pie chart?
Avoid pie charts when: (1) you have too many categories (more than 8), (2) categories have very similar values (hard to distinguish), or (3) you need to show changes over time (use line graphs instead).
Q9. How do you find the value from a pie chart angle?
Value = (Angle / 360°) × Total. For example, if the total is 500 and a sector angle is 72°, then Value = (72/360) × 500 = 100.
Q10. What does a half-circle sector represent?
A half-circle sector has an angle of 180°, which represents exactly 50% of the total data.
