Pie Charts — Summary
A pie chart splits a whole into sectors, each a share of 100% (or 360°). Placement DI uses pies for budget/market-share breakdowns, and the degree ⇄ percentage conversion is the essential tool.
Key conversions
- Whole circle = 360° = 100%.
- Percentage → degrees: multiply by 3.6 (25% = 90°).
- Degrees → percentage: divide by 3.6 (72° = 20%).
- Sector value = (sector % ) × total.
| Convert | Rule | Example |
|---|---|---|
| % → degrees | × 3.6 | 25% = 90° |
| degrees → % | ÷ 3.6 | 72° = 20% |
| sector value | % × total | 20% of 5000 = 1000 |
| two sectors' ratio | ratio of their % (or degrees) | 30:20 = 3:2 |
Example: a 90° sector is 25% of the whole; if the total is 4000, that sector = 1000. ✓
Exam Tricks & Tips
- 🎯 Convert with 3.6: percentage × 3.6 = degrees, degrees ÷ 3.6 = percentage.
- 🎯 A sector's value = its percentage × the given total.
- 🎯 Ratio of two sectors = ratio of their percentages (or degrees) directly.
- 🎯 If given degrees, you can compare sectors without converting to percentage.
- 🎯 Two pies with different totals: convert to actual values before comparing.
- ❌ Don't compare percentages across two pie charts with different totals as if they were absolute values.
Expected exam pattern: sector value, degree-percentage conversion, ratio between sectors, and two-pie comparisons. 3 to 5 questions, ~50 seconds each.
Quick recap: 360° = 100%; percentage × 3.6 = degrees; sector value = percentage × total; compare across pies only via actual values.
Pie Charts — Flashcards
Q1. A full pie equals how many degrees?
A1. 360° (= 100%).
Q2. Convert 25% to degrees.
A2. 25 × 3.6 = 90°.
Q3. Convert 72° to percentage.
A3. 72 ÷ 3.6 = 20%.
Q4. Sector value formula?
A4. Sector percentage × total.
Q5. 20% of a total of 5000?
A5. 1000.
Q6. A 90° sector is what percent?
A6. 25%.
Q7. Ratio of a 30% and 20% sector?
A7. 3:2.
Q8. Multiplier for % → degrees?
A8. 3.6.
Q9. Comparing two pies with different totals — do what first?
A9. Convert to actual values.
Q10. A 90° sector of a total 4000?
A10. 25% × 4000 = 1000.
Q11. Can you compare sectors using degrees directly?
A11. Yes — within the same pie.
Q12. Divisor for degrees → percentage?
A12. 3.6.
Pie Charts
Pie charts show how a whole splits into parts, using either percentages or degrees (the full circle = 100% = 360°). The one conversion — degrees to percent — unlocks every pie-chart question.
What this topic tests: converting between degrees, percentages and actual values, and combining a pie chart with a given total.
The method
Beginner — the whole is 100% = 360°
Each slice is a fraction of the whole. If a slice is given in degrees, its share = degrees/360 × 100 percent. If given in percent, its degrees = percent/100 × 360. And 1% = 3.6°.
Intermediate — from share to actual value
When the total value is given (e.g. total expenditure ₹80,000), a slice's actual value = share% × total. A 25% slice of ₹80,000 = ₹20,000. Ratios between slices equal the ratios of their angles or percentages directly.
Advanced — two pies and combined questions
- Comparing two slices: their ratio = ratio of their angles/percentages (the common total cancels).
- Two pie charts (e.g. two companies) with different totals: convert each slice to an actual value before comparing across pies — you cannot compare percentages of different totals directly.
- "By what percent is slice A more than slice B" = (A − B)/B × 100 on their actual values.
Worked example
In a pie chart of a family's monthly budget, "Food" is 90° and the total budget is ₹36,000. Find the amount spent on food.
Food share = 90/360 = 1/4 = 25%. Amount = 25% of 36,000 = ₹9,000. (Using 1° = ₹36,000/360 = ₹100, so 90° = ₹9,000 — same answer.)
Where it appears
TCS NQT, Infosys, Wipro, Cognizant, Capgemini DI; pie charts are a standard DI set, sometimes paired with a table of totals.
Speed tricks and shortcuts
- 1% = 3.6°; 1° = total/360 in value.
- Slice ratios = angle ratios = percentage ratios (same total).
- Across two pies with different totals, compare actual values, not percentages.
- Mnemonic: "Whole = 360° = 100%; degrees over 360 gives the share."
Comparing percentages across two different pies as if equal. A 30% slice of a ₹1,00,000 total is larger than a 40% slice of a ₹50,000 total. Convert to actual values before comparing across charts.
- ✓- Full circle = 100% = 360°; 1% = 3.6°.
- ✓- Slice value = share% × total (or degrees × total/360).
- ✓- Slice ratios equal angle/percentage ratios within one pie.
- ✓- Across pies, compare actual values, not percentages.
- ✓Treat the pie as 100% = 360°, convert a slice's degrees to a share, and multiply by the total for actual values. When two pies have different totals, always compare rupee values, not percentages.
Pie Charts — Formula Sheet
Key formulas
- Central angle of a sector = (value/total)×360°; value = (angle/360)×total.
- Percentage share = (value/total)×100 = angle/3.6.
- Whole circle = 360° = 100% of the total.
- Compare sectors by their angles or percentages.
- Combine with a given total to get absolute values.
- ✓- Angle = (value/total)×360°.
- ✓- Percentage = angle/3.6.
- ✓- Value = (angle/360)×total.
- ✓- Full circle = 360° = 100%.
Usage: divide a sector's angle by 3.6 to get its percentage share.
Pie Charts — Worked Example
Worked Example
Problem: A family's monthly income of ₹60,000 is distributed as shown in a pie chart:
Rent 30%, Food 25%, Education 15%, Savings 20%, Others 10%.
(a) How much more is spent on Rent than on Education? (b) What is the central angle of the "Food" sector?
Solution: (a) Convert each percentage to rupees of the ₹60,000 income.
- Rent = 30% of 60,000 = 18,000
- Education = 15% of 60,000 = 9,000
- Difference = 18,000 − 9,000 = ₹9,000.
(b) A full pie is 360°, so each percentage maps to (percentage × 360)/100 degrees.
- Food = (25 × 360)/100 = 90°.
Answer: Rent exceeds Education by ₹9,000; the Food sector's central angle is 90°.
- ✓- Convert a percentage share to a value: (percent/100) × total amount.
- ✓- Sector angle = (percentage/100) × 360°; the whole pie is always 360°.
- ✓- All the slices must sum to 100% (and 360°) — a quick consistency check.