Pie Charts

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.

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 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."

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.

Usage: divide a sector's angle by 3.6 to get its percentage share.

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°.