To calculate a percentage, divide the part by the whole and multiply by 100: percentage = (part ÷ whole) × 100. So 45 marks out of 60 is 45 ÷ 60 × 100 = 75%. To find a percentage of a number, turn the percentage into a decimal and multiply: 18% of 1,500 = 0.18 × 1,500 = 270.
Almost every percentage sum is a variation on those two lines. Below are the formulas for the six most common questions, each with a worked example and the mistakes people often make. Our percentage calculator handles all six and shows the working, step by step.
Tools used in this guide
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The six percentage formulas at a glance
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | (X ÷ 100) × Y | 18% of 1,500 = 270 |
| X is what % of Y? | (X ÷ Y) × 100 | 45 of 60 = 75% |
| % change from A to B | (B − A) ÷ A × 100 | 80 → 100 = +25% |
| Increase Y by X% | Y × (1 + X ÷ 100) | 1,500 + 18% = 1,770 |
| Decrease Y by X% | Y × (1 − X ÷ 100) | 2,999 − 30% = 2,099.30 |
| Y is X% of what? | Y ÷ (X ÷ 100) | 540 is 45% of 1,200 |
Percentages, decimals and fractions
Most percentage sums get easier once you know a few common conversions by heart. To turn a percentage into a decimal, divide by 100. To go back, multiply by 100.
| Percentage | Decimal | Fraction |
|---|---|---|
| 1% | 0.01 | 1/100 |
| 5% | 0.05 | 1/20 |
| 10% | 0.1 | 1/10 |
| 12.5% | 0.125 | 1/8 |
| 20% | 0.2 | 1/5 |
| 25% | 0.25 | 1/4 |
| 33.33% | 0.3333 | 1/3 |
| 50% | 0.5 | 1/2 |
| 75% | 0.75 | 3/4 |
So 25% off is the same as paying three-quarters of the price, and 12.5% of 800 is simply 800 ÷ 8 = 100.
What is X% of Y?
Divide the percentage by 100 to get a decimal, then multiply.
Example: 18% GST on a ₹1,500 bill. 18 ÷ 100 = 0.18, and 0.18 × 1,500 = ₹270.
Example: a 15% tip on a ₹2,400 restaurant bill. 0.15 × 2,400 = ₹360, so you'd pay ₹2,760 in all.
Two shortcuts help with mental maths:
- Build from 10%. 10% of 1,500 is 150 (move the decimal point one place left). 20% is double that, 300, and 5% is half, 75.
- Swap the numbers. X% of Y equals Y% of X. 8% of 50 looks awkward, but 50% of 8 is obviously 4.
X is what percent of Y?
Divide the part by the whole, then multiply by 100.
Example: you've saved ₹12,000 towards a ₹50,000 goal. 12,000 ÷ 50,000 = 0.24, and 0.24 × 100 = 24%. You have 76% still to go.
Tip: The "whole" always goes on the bottom. If you're unsure which number is the whole, ask "percentage of what?" The answer to that is your divisor.
Percentage increase and decrease
Find the difference, divide by the original (old) value, and multiply by 100.
Increase: a price goes from ₹80 to ₹100. The difference is 20, and 20 ÷ 80 × 100 = 25% increase.
Decrease: a price goes from ₹100 to ₹80. The difference is −20, and −20 ÷ 100 × 100 = 20% decrease.
Same two prices, different answers. Each time you divide by the value you started from. That's also why a 20% drop needs a 25% rise to get back to where you were.
Salary hike: ₹6,00,000 to ₹7,20,000 is a difference of ₹1,20,000. 1,20,000 ÷ 6,00,000 × 100 = 20% hike.
If the old value is zero, there's no percentage change. Anything divided by zero is undefined, so give the difference in units instead.
Adding or removing a percentage (GST, tips, discounts)
Adding a percentage
Multiply by (1 + rate). To add 18% GST to ₹1,500: 1,500 × 1.18 = ₹1,770. That's the same as working out the ₹270 of GST and adding it on, but in one step.
Taking a discount off
Multiply by (1 − rate). A ₹2,999 item at 30% off costs 2,999 × 0.70 = ₹2,099.30, a saving of ₹899.70. The discount calculator does this, and flat-amount discounts too.
Removing GST from a price that already includes it
Divide by (1 + rate). Don't subtract the rate.
Example: ₹1,770 including 18% GST.
- Price before GST = 1,770 ÷ 1.18 = ₹1,500
- GST inside = 1,770 × 18 ÷ 118 = ₹270
Warning: Taking 18% off ₹1,770 gives ₹1,451.40, which is wrong. The 18% was charged on ₹1,500, not on ₹1,770. Our GST and sales tax calculator has a "price includes tax" option that does the division for you. It also splits the tax into CGST and SGST halves.
Reverse percentage: finding the original number
When you know the result and the percentage it represents, divide by the percentage as a decimal.
Example 1: 540 is 45% of what? 540 ÷ 0.45 = 1,200. Check: 45% of 1,200 is 540.
Example 2: a sale price is ₹2,099 after 30% off. What was the original price? After a 30% discount you pay 70%, so 2,099 ÷ 0.70 = ₹2,998.57. The shop probably listed it at ₹2,999 and rounded the sale price.
Removing GST is the same idea: a GST-inclusive price is 118% of the base price, so you divide by 1.18.
In the percentage calculator, the reverse mode takes the known value and the percentage it is (70 for "30% off", 118 for "18% GST included").
Marks percentage and CGPA
Marks percentage = marks obtained ÷ total marks × 100.
| Marks | Calculation | Percentage |
|---|---|---|
| 432 out of 500 | 432 ÷ 500 × 100 | 86.4% |
| 1,080 out of 1,200 | 1,080 ÷ 1,200 × 100 | 90% |
| 67 out of 80 | 67 ÷ 80 × 100 | 83.75% |
Always use the grand total for the papers you're averaging. Don't average the subject percentages if the subjects have different maximum marks, because that gives the wrong answer.
CGPA to percentage (CBSE convention): percentage = CGPA × 9.5. A CGPA of 9.2 is 9.2 × 9.5 = 87.4%. To go the other way, divide by 9.5: 86.4% is roughly a 9.09 CGPA.
Note: The 9.5 multiplier is CBSE's convention. Many universities and other boards use a different formula, or none at all. Use the one printed on your marksheet or in the admission rules you're applying under.
Common percentage mistakes
Percentage vs percentage points
If a loan's rate goes from 8% to 9%, it has risen by 1 percentage point. As a percentage of the old rate, that's (9 − 8) ÷ 8 × 100 = 12.5%. Both statements are true, but they mean different things. Use "percentage points" when you compare two percentages directly.
A rise and an equal fall don't cancel out
₹1,000 up 10% is ₹1,100. Then 10% off ₹1,100 is ₹990, not ₹1,000. The same thing happens in reverse: ₹5,000 up 20% and then down 20% ends at ₹4,800.
Stacked discounts don't add up
"20% off plus an extra 10%" is not 30% off. The second discount applies to the already-reduced price: 0.80 × 0.90 = 0.72, so you pay 72%. The total discount is 28%. To get it right, run the discount calculator twice.
Mixing up markup and margin
A shop buys an item for ₹800 and sells it for ₹1,000. The ₹200 profit is a 25% markup on cost (200 ÷ 800). It's only a 20% margin on the selling price (200 ÷ 1,000). Shopkeepers usually quote markup and accountants usually quote margin, so ask which one is meant.
Dividing by the wrong base
For percentage change, divide by the old value. For "what percent of", divide by the whole. Most wrong answers come from putting the wrong number on the bottom.
Rounding too early
Keep the full decimal until the last step. 1 ÷ 3 is 0.3333, which gives 33.33%. Rounding to 0.3 first gives 30%, a big error once you multiply by a large amount.