In this guide
A pie chart shows how one total is split. Every sector is a share, so every question comes down to a small set of moves: degrees to percentages, percentages to values, and, when there are two pies, adjusting for the change in the total.
The format looks easy, and the single-pie questions usually are. The marks are lost when a set has two pies with different totals, because the eye compares angles and the question asks about amounts. This guide covers the conversions, one rule that answers many two-pie questions instantly, and a worked set. The pies are described as tables, since this page cannot show images.
The conversions
A full circle is 360°, and it stands for 100% of the total.
- Degrees to percentage: divide by 3.6. So 72° = 20%.
- Percentage to degrees: multiply by 3.6. So 15% = 54°.
- Degrees to value: value per degree = total ÷ 360; multiply by the angle.
| Degrees | Percentage | Degrees | Percentage |
|---|---|---|---|
| 18° | 5% | 90° | 25% |
| 36° | 10% | 108° | 30% |
| 45° | 12.5% | 120° | 33.33% |
| 54° | 15% | 144° | 40% |
| 60° | 16.67% | 180° | 50% |
| 72° | 20% | 216° | 60% |
Why you cannot compare two pies by angle
A sector can shrink while its value grows, if the total grows enough. A sector can grow while its value falls, if the total shrinks. The angle tells you the share, never the amount, unless the totals are equal.
The share-and-growth rule. If a sector's share goes up from one pie to the next, that item grew faster than the total. If its share stays the same, it grew at exactly the total's rate. If its share goes down, it grew slower than the total (and may still have grown). This follows from share = item ÷ total: the share rises only when the item rises faster than the total.
This rule answers "how many items grew faster than the total" questions without calculating a single value.
Worked set: a household budget over two years
Two pie charts show how a household spent its annual budget in 2024 and 2025. The total budget was ₹5,40,000 in 2024 and ₹7,20,000 in 2025. The central angles are below.
| Head | 2024 angle | 2025 angle |
|---|---|---|
| Rent | 90° | 80° |
| Food | 72° | 70° |
| Education | 54° | 64° |
| Transport | 36° | 36° |
| Health | 18° | 20° |
| Savings | 90° | 90° |
| Total | 360° | 360° |
Value of 1°: 2024: 5,40,000 ÷ 360 = ₹1,500. 2025: 7,20,000 ÷ 360 = ₹2,000.
| Head | 2024 amount | 2025 amount | Change |
|---|---|---|---|
| Rent | ₹1,35,000 | ₹1,60,000 | +18.52% |
| Food | ₹1,08,000 | ₹1,40,000 | +29.63% |
| Education | ₹81,000 | ₹1,28,000 | +58.02% |
| Transport | ₹54,000 | ₹72,000 | +33.33% |
| Health | ₹27,000 | ₹40,000 | +48.15% |
| Savings | ₹1,35,000 | ₹1,80,000 | +33.33% |
| Total | ₹5,40,000 | ₹7,20,000 | +33.33% |
Q1. How much did the household spend on education in 2025?
- 64 × ₹2,000 = ₹1,28,000.
Q2. Rent's angle fell from 90° to 80°. What happened to the amount spent on rent?
- 2024: 90 × 1,500 = ₹1,35,000. 2025: 80 × 2,000 = ₹1,60,000.
- It rose by about 18.5% ((1,60,000 − 1,35,000) ÷ 1,35,000 = 25,000 ÷ 1,35,000 ≈ 0.185). The smaller slice is a bigger amount.
Q3. For how many heads did spending grow by a higher percentage than the total budget?
- The total grew by (7,20,000 − 5,40,000) ÷ 5,40,000 = 1/3, or 33.33%.
- By the share-and-growth rule, only heads whose angle increased qualify: Education (54° to 64°) and Health (18° to 20°).
- Transport and Savings kept the same angle, so they grew at exactly 33.33%, which is not "higher".
- Answer: 2. The table confirms it: 58.02% and 48.15%.
Q4. In 2026 the total budget rises by 10%, and the amount saved stays at ₹1,80,000. What is the central angle for Savings in 2026, to one decimal place?
- Total 2026 = 7,20,000 × 1.1 = ₹7,92,000.
- Angle = 1,80,000 ÷ 7,92,000 × 360 ≈ 0.2273 × 360 ≈ 81.8°.
Q5 (TITA). By how many rupees did combined spending on Education and Health rise from 2024 to 2025?
- 2024: 81,000 + 27,000 = 1,08,000. 2025: 1,28,000 + 40,000 = 1,68,000.
- Rise: 60,000.
- Faster route: 2025 combined angle is 84°, so 84 × 2,000 = 1,68,000; 2024 combined angle is 72°, so 72 × 1,500 = 1,08,000.
Pies with percentages instead of degrees
Many pies are labelled in percentages. The method is the same, with value per 1% = total ÷ 100. A company with a ₹50 lakh budget split 40% salaries, 20% marketing, 25% operations and 15% research spends 20% × 50 = ₹10 lakh on marketing, and its operations sector has a central angle of 25% × 360° = 90°.
"By what percentage is the salaries budget more than research?" is a comparison inside one pie, so the total cancels: (40 − 15) ÷ 15 = 25 ÷ 15 ≈ 166.7%.
Common traps
- Comparing angles across pies with different totals. Convert to values, or use the share-and-growth rule.
- Percentage versus percentage points. Food's share fell from 20% to 19.44%, a drop of 0.56 percentage points, while food spending rose 29.63%.
- "Higher" versus "at least". Items with an unchanged share grew at exactly the total's rate.
- Rounding degrees too early. Keep fractions like 1/3 and 2/9 exact until the last step.
Practice set
- What central angle represents 12.5% of a total?
- Using the household set, what is the ratio of Savings in 2025 to Rent in 2024?
- In 2026 the household spends ₹90,000 on transport out of a total of ₹8,00,000. What is the central angle for transport, to one decimal place?
- Using the household set, by how many percentage points did the share of Education change from 2024 to 2025?
Answers:
- 45°. 12.5 × 3.6 = 45.
- 4 : 3. 1,80,000 : 1,35,000, dividing both by 45,000.
- 40.5°. 90,000 ÷ 8,00,000 = 0.1125; × 360 = 40.5.
- Up about 2.78 percentage points. 54° is 15%; 64° is 64 ÷ 3.6 ≈ 17.78%.
What to do next
- Learn the degree table until 45°, 60°, 108° and 144° convert without thinking.
- For every two-pie set, write the value of 1° for each pie before reading the questions.
- Apply the share-and-growth rule to three old two-pie sets and check how many questions it answers on its own.
- Next, practise turning paragraph data into tables with caselets, and revisit bar and line charts for growth-rate traps.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Indian Institutes of Management website .
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