What a percentage actually is
A percentage is a fraction with 100 fixed as the denominator. "Per cent" is Latin for "by the hundred", so 25% is another way of writing 25/100, or 0.25. That is the whole idea, and every percentage problem reduces to it.
The practical consequence is that you can always convert in three directions. To turn a percentage into a decimal, divide by 100. To turn a decimal into a percentage, multiply by 100. To turn a fraction into a percentage, divide top by bottom, then multiply by 100.
| Percentage | Decimal | Fraction |
|---|---|---|
| 1% | 0.01 | 1/100 |
| 5% | 0.05 | 1/20 |
| 10% | 0.10 | 1/10 |
| 20% | 0.20 | 1/5 |
| 25% | 0.25 | 1/4 |
| 33.33% | 0.3333 | 1/3 |
| 50% | 0.50 | 1/2 |
| 75% | 0.75 | 3/4 |
| 100% | 1.00 | 1 |
| 150% | 1.50 | 3/2 |
The six formulas
1. What is X% of Y?
- X
- The percentage
- Y
- The number you are taking a percentage of
15% of 200 = 0.15 × 200 = 30.
2. X is what percent of Y?
30 is what percent of 200? 30 ÷ 200 × 100 = 15%.
3. Percentage increase or decrease
From 200 to 230: (230 − 200) ÷ 200 × 100 = +15%. A negative result means a decrease.
4. Add a percentage to a number
200 plus 15% = 200 × 1.15 = 230.
5. Subtract a percentage from a number
200 minus 15% = 200 × 0.85 = 170.
6. Percentage difference between two numbers
This one is different from percentage change. Change has a direction — a starting point and an end point. Difference is symmetric: it compares two values neither of which came first, using their average as the reference. Between 200 and 230 the difference is 13.95%, while the change from 200 to 230 is 15%.
Three mistakes that cost real money
Percentage increases and decreases do not cancel out
A ₹1,000 item marked up 20% becomes ₹1,200. Discount that by 20% and you get ₹960, not ₹1,000. The 20% off applies to the larger number, so it removes more than the markup added.
To reverse a 20% increase you need a 16.67% decrease. In general, to undo an increase of X% you need a decrease of X ÷ (100 + X) × 100.
Percentage points are not percentages
If an interest rate rises from 4% to 6%, that is a rise of 2 percentage points, but a 50% increase in the rate. Both are correct statements about the same change, and confusing them is a common way to make a small change sound large.
Successive discounts do not add
"30% off, then an extra 20% off" is not 50% off. The second discount applies to the already-reduced price: 0.70 × 0.80 = 0.56, so it is 44% off. On a ₹5,000 item that is ₹2,800 rather than ₹2,500 — a ₹300 difference.
Percentages in everyday situations
| Situation | Question | Formula |
|---|---|---|
| Restaurant tip | What is an 18% tip on ₹1,450? | X% of Y |
| Sale price | What does a 30% discount leave? | Subtract % |
| Exam score | 42 out of 60 is what grade? | X is what % of Y |
| Salary rise | Old ₹50,000, new ₹57,500 — what rise? | % change |
| Adding tax | Price plus 18% GST | Add % |
| Comparing two prices | How far apart are ₹240 and ₹260? | % difference |
For the money-specific versions of these, see the tip calculator, the discount calculator and the GST calculator. For exam marks, the grade calculator handles weighted components.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 to get a decimal, then multiply by the number. For 15% of 200: 15 ÷ 100 = 0.15, and 0.15 × 200 = 30.
The mental shortcut is to find 10% first by moving the decimal point one place left, then scale. 10% of 200 is 20, so 5% is 10, and 15% is 30.
What is the difference between percentage change and percentage difference?
Percentage change measures movement from a starting value to an ending value, and the direction matters. Percentage difference compares two values symmetrically against their average, and gives the same answer whichever order you put them in.
Use change for "my salary went from X to Y". Use difference for "these two quotes are X apart".
How do I work out the original price before a discount?
Divide the sale price by (1 − discount ÷ 100). An item sold for ₹700 after 30% off had an original price of 700 ÷ 0.70 = ₹1,000.
The same logic applies to removing tax: divide rather than subtract, because the percentage was applied to the smaller base.
Can a percentage be more than 100?
Yes. 100% is simply the whole, so 150% is one and a half times it. A value that triples has increased by 200% — it gained twice its original amount on top of what it already had.
Percentage decreases, though, cannot exceed 100%, since you cannot remove more than everything.
How do I calculate a percentage in reverse?
If you know the result and the percentage, divide rather than multiply. If 30 is 15% of a number, that number is 30 ÷ 0.15 = 200.
Switch this calculator to "X is what % of Y" to check any answer both ways.