The three percentage formulas you need
Almost every percentage question is one of three simple formulas. "Percent" means "per hundred", so every formula divides or multiplies by 100.
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | X ÷ 100 × Y | 15% of 80 = 12 |
| X is what percent of Y? | X ÷ Y × 100 | 30 of 120 = 25% |
| Percentage change from X to Y | (Y − X) ÷ |X| × 100 | 50 → 65 = +30% |
Worked examples
Tip on a bill: 18% of $64 = 0.18 × 64 = $11.52.
Test score: you answered 42 of 48 questions correctly. 42 ÷ 48 × 100 = 87.5%.
Price increase: rent rises from $1,500 to $1,620. (1,620 − 1,500) ÷ 1,500 × 100 = 8% increase.
Sale price: a $250 jacket at 30% off costs 250 × (1 − 0.30) = $175. For shopping questions our discount calculator also shows how much you save.
Percentage change vs percentage points
When a rate moves from 4% to 5%, it rose by 1 percentage point but by 25 percent (because 1 is 25% of 4). News reports about interest rates, unemployment and polls should use "percentage points" for the simple difference — mixing the two is one of the most common mistakes with percentages.
Why +50% and −50% don't cancel out
Percentage changes are measured from the starting value, so they are not symmetric. If a $100 stock rises 50% it reaches $150; if it then falls 50% it drops to $75, not back to $100. To undo a percentage increase of p%, you need a decrease of p ÷ (100 + p) × 100 percent — undoing a 50% rise takes a 33.3% fall.
Quick mental math tricks
- 10% — move the decimal point one place left (10% of 230 = 23).
- 5% — half of 10% (5% of 230 = 11.5).
- 1% — move the decimal point two places (1% of 230 = 2.3).
- Swap trick — X% of Y equals Y% of X, so 8% of 50 is the same as 50% of 8 = 4.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For example, 20% of 150 = 0.20 × 150 = 30.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. For example, 45 out of 60 = 45 ÷ 60 × 100 = 75%.
How do I calculate percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. A change from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25%.
Can a percentage be more than 100%?
Yes. A value can be more than its reference — 150 is 150% of 100 — and prices can rise by more than 100%. Only percentages of a fixed whole, like the share of a test answered correctly, are capped at 100%.
How do I reverse a percentage to find the original number?
Divide the final number by (1 + p ÷ 100). If a price after a 20% markup is $96, the original was 96 ÷ 1.20 = $80.
Last updated: October 8, 2026