How to Calculate Percentage: Every Common Type Explained
Percentages appear everywhere — discounts, exam marks, interest, tips, statistics. The word percent literally means 'per hundred', so a percentage is just a fraction with 100 on the bottom. Once you see that, every percentage problem becomes one of a few simple patterns.
1. Percentage of a number
To find a percentage of a number, convert the percentage to a decimal and multiply. 20% of 250 = 0.20 × 250 = 50. The trick is dividing the percentage by 100 first: 20% becomes 0.20, 7.5% becomes 0.075, and so on.
2. What percentage one number is of another
To find what percentage A is of B, divide A by B and multiply by 100. If you scored 42 out of 50, that is 42 ÷ 50 × 100 = 84%. This is exactly how exam marks become a percentage.
3. Percentage change (increase or decrease)
Percentage change tells you how much something grew or shrank. The formula is: change = (new − old) ÷ old × 100. If a price rose from ₹800 to ₹1,000, the change is (1000 − 800) ÷ 800 × 100 = 25% increase. If it fell from ₹1,000 to ₹800, that is (800 − 1000) ÷ 1000 × 100 = −20%. Note the answers differ — a 25% rise followed by a 20% fall returns you to the start, which surprises many people.
4. Reverse percentage (finding the original)
Sometimes you know the result after a percentage was applied and want the original. If a price after a 20% discount is ₹640, divide by (1 − 0.20): ₹640 ÷ 0.80 = ₹800 original. The same logic in reverse handles tax-inclusive prices and markups.
Quick mental-maths shortcuts
- 10% of a number: just move the decimal one place left. 10% of 540 = 54.
- 5% is half of 10%. So 5% of 540 = 27.
- 1% moves the decimal two places. 1% of 540 = 5.4.
- To find 15%, add 10% and 5% together. Build any percentage from these blocks.
- x% of y always equals y% of x — so 18% of 50 is the same as 50% of 18 = 9, which is easier.
Common mistakes to avoid
The biggest error is subtracting a percentage to reverse it. Removing a 20% increase is not subtracting 20% — you divide by 1.20. The second common slip is comparing percentage points with percentages: a rise from 10% to 12% is a 2 percentage-point rise but a 20% relative increase. Being precise about which one you mean prevents confusion.
Percentages in everyday situations
The same four patterns cover almost every real situation. Splitting a restaurant bill with an 18% tip uses 'percentage of a number'. Turning your exam marks into a result uses 'one number as a percentage of another'. Reading that rent rose from ₹15,000 to ₹16,500 uses 'percentage change' — a 10% rise. And finding the pre-sale price from a discounted tag uses 'reverse percentage'. Recognising which of the four a problem fits is most of the work; the arithmetic that follows is always the same.
Percentage points vs percent — a costly confusion
Headlines often blur these. If an interest rate moves from 6% to 9%, that is a 3 percentage-point increase but a 50% relative increase. Both statements are true, yet they mean very different things, and real money decisions have been made badly on exactly this slip. Whenever you read or quote a change, ask whether it is points or a relative percent before you act on it.
Compounding percentages don't simply add
A 10% rise followed by another 10% rise is not a 20% rise — it is 1.10 × 1.10 = 1.21, or 21%, because the second rise applies to the already-larger number. The same is true of successive discounts: 20% off then 10% off is 0.80 × 0.90 = 0.72, a 28% total discount, not 30%. Multiply the factors; never add the percentages.
Frequently asked questions
How do I add a percentage to a number quickly?
Multiply by 1 plus the rate as a decimal. To add 15%, multiply by 1.15; to add 8%, multiply by 1.08.
How do I find the original price before a discount?
Divide the sale price by 1 minus the discount as a decimal. A ₹640 tag after 20% off was ₹640 ÷ 0.80 = ₹800 originally.
How do I turn a fraction into a percentage?
Divide the top by the bottom and multiply by 100. So 3/8 = 0.375 × 100 = 37.5%.
The bottom line
Almost every percentage question is one of four patterns: a percentage of a number, one number as a percentage of another, a percentage change, or a reverse percentage. Learn those four and the rest is just plugging in numbers. For anything fiddly, our calculator shows the working so you can check yourself.