The three formulas, once and for all
Each mode above uses one of these:
- X% of a number: (X ÷ 100) × number. A 20% discount on ₹1,500 takes off ₹300, so you pay ₹1,200.
- X is what % of Y: (X ÷ Y) × 100. Scoring 450 out of 600 is (450 ÷ 600) × 100 = 75%.
- Percentage change: ((new − old) ÷ old) × 100. A salary moving from ₹40,000 to ₹52,000 is a 30% hike.
The traps people fall into
Percentage change is directional: a 50% increase followed by a 50% decrease does not bring you back — ₹100 grows to ₹150, then falls to ₹75. This is why a stock that drops 50% needs a 100% gain to recover, and why 'average' percentage returns can mislead.
Percentages don't add across different bases either. A 10% service charge plus 5% GST on a restaurant bill isn't 15% on the food — the GST may be calculated on the service-charge-included amount, depending on the bill. When percentages stack, compute them step by step.
And a percentage point is not a percent: if inflation moves from 4% to 6%, it rose 2 percentage points but 50 percent. News headlines regularly blur this — now you won't.
Everyday Indian uses
The same three modes cover nearly everything:
- Students: marks percentage, attendance percentage (75% rule), percentile vs percentage (they are different — percentile is your rank position, not your score).
- Shopping: discount amounts, comparing '40% off' against 'flat ₹500 off' on a given price.
- Salary: hike percentage between CTC offers; what a 30% hike means in rupees.
- GST arithmetic: 18% GST on ₹2,499 adds ₹449.82 — mode one answers it directly.
Frequently asked questions
›How do I calculate the percentage of marks?
Divide marks obtained by total marks and multiply by 100. Scoring 450 out of 600 gives (450 ÷ 600) × 100 = 75%. Use the second calculator above — enter marks scored and total marks.
›How do I calculate a percentage increase like a salary hike?
Subtract the old value from the new, divide by the old value, multiply by 100. From ₹40,000 to ₹52,000: (12,000 ÷ 40,000) × 100 = 30% hike. The third calculator above does this and tells you whether it's an increase or a decrease.
›What is the difference between percentage and percentile?
Percentage measures your score: 450/600 = 75%. Percentile measures your position: a 95th percentile means you scored better than 95% of test-takers. Exams like JEE and CAT report percentiles, which is why a 99 percentile doesn't mean 99% marks.
›How do I calculate a discount percentage?
For a known discount percent, use mode one: 20% of ₹1,500 = ₹300 off. To find what percent a discount is, use mode two: ₹300 off ₹1,500 is (300 ÷ 1500) × 100 = 20%. To compare two discounted prices, compute both final prices.
›Why doesn't a 50% loss cancel a 50% gain?
Because each percentage applies to a different base. ₹100 up 50% is ₹150; ₹150 down 50% is ₹75. The bigger the swing, the bigger the asymmetry — a 90% loss needs a 900% gain to recover. This matters for investments more than exams.