Solve any everyday percentage question: what is X% of a number, what percent one number is of another, and the percentage increase or decrease between two values.
Percentage formulas
"Percent" means "per hundred", so 15% is 15/100 = 0.15.
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | X ÷ 100 × Y | 15% of 80 = 12 |
| X is what % of Y? | X ÷ Y × 100 | 30 is 25% of 120 |
| % change from X to Y | (Y − X) ÷ X × 100 | 80 to 95 = +18.75% |
| Increase Y by X% | Y × (1 + X ÷ 100) | 80 + 15% = 92 |
A common mistake: percentage points
If an interest rate rises from 4% to 5%, it went up by 1 percentage point, but by 25 percent (1 ÷ 4). Both are correct, so be clear which one you mean.
Why a 50% loss needs a 100% gain
Percentage changes are not symmetrical. If $100 falls 50% to $50, it must rise 100% to get back to $100, because the second change is measured from a smaller starting point.
Quick mental math tricks
- 10%: move the decimal point one place left. 10% of 86 is 8.6.
- 5%: half of 10%.
- Swap trick: X% of Y equals Y% of X. 8% of 50 is the same as 50% of 8, which is 4.
Frequently asked questions
How do I find the original price before a percentage increase?
Divide by (1 + the percentage). A price of $115 after a 15% increase was $115 ÷ 1.15 = $100.
What is the difference between percentage change and percentage difference?
Change compares a new value with an old one. Difference compares two values without a "before" and "after". See the percentage difference calculator.
Related tools
Results are estimates for planning and education only. They are not financial, tax, legal or medical advice. Check important numbers with a qualified professional.