Four percentage problems, solved
This page handles the four calculations people search for most:
- What is X% of Y? — e.g. a 15% tip on $200, or 7% sales tax on a purchase.
- X is what percent of Y? — e.g. you scored 42 out of 50 on a test.
- Percentage change from X to Y — e.g. rent went from $1,600 to $1,750.
- Price after a discount — e.g. a $80 jacket at 25% off.
Type your numbers and the answers update instantly. Results are rounded to four decimal places.
The formulas
| Question | Formula |
|---|---|
| X% of Y | Y × X ÷ 100 |
| X is what % of Y | X ÷ Y × 100 |
| Change from X to Y | (Y − X) ÷ X × 100 |
| Y after X% off | Y × (1 − X ÷ 100) |
The trick with all of them is remembering that “percent” literally means “per hundred”. A percentage is just a fraction with 100 on the bottom, so converting between percentages and decimals is a matter of moving the decimal point two places: 35% = 0.35, 0.08 = 8%.
Worked examples
- Sales tax: a $649 laptop with 8.25% tax. 649 × 8.25 ÷ 100 = $53.54 tax, $702.54 total.
- Test score: 42 correct out of 50. 42 ÷ 50 × 100 = 84%.
- Raise: salary goes from $58,000 to $62,000. (62,000 − 58,000) ÷ 58,000 × 100 = +6.9%.
- Discount: a $120 pair of shoes at 30% off. 120 × 0.70 = $84, saving $36.
Mental math shortcuts
- 10% — move the decimal one place left. 10% of $84 is $8.40.
- 5% — half of 10%. 5% of $84 is $4.20.
- 15% — 10% + 5%. 15% of $84 is $12.60.
- 20% — double 10%. 20% of $84 is $16.80.
- 25% — divide by 4. 25% of $84 is $21.
- X% of Y = Y% of X. 8% of 50 is the same as 50% of 8 = 4. Sometimes flipping makes the arithmetic trivial.
A common mistake: reversing a percentage change
If a price rises 20% and then falls 20%, it does not return to the original. $100 → $120 → $96. To undo a 20% increase you need a 16.7% decrease (1 ÷ 1.2 = 0.833). The percentage-change calculator above will confirm it.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. 15% of 200 is 200 × 15 ÷ 100 = 30.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. 30 out of 200 is 30 ÷ 200 × 100 = 15%.
How do I calculate percentage change?
Subtract the old value from the new one, divide by the old value, and multiply by 100. From 200 to 250 is (250 − 200) ÷ 200 × 100 = +25%. A negative result means a decrease.
What's the difference between percentage points and percent?
Going from 10% to 15% is an increase of 5 percentage points but a 50 percent increase (because 15 is 50% more than 10). Keep the two straight when reading news about rates.
Last updated August 26, 2026.