Three percentage formulas
"Percent" means "per hundred", so 15% is 15 out of 100, or 0.15. Almost every percentage problem is one of these three:
X% of Y = (X ÷ 100) × YX is what % of Y = (X ÷ Y) × 100% change = (new − old) ÷ old × 100
Worked examples
- 15% of 240 = 0.15 × 240 = 36.
- 45 is what percent of 180? 45 ÷ 180 = 0.25, so 25%.
- A price goes from $80 to $92. (92 − 80) ÷ 80 × 100 = 15% increase.
- Finding the original. If a sale price of $68 is 15% off, the original is $68 ÷ 0.85 = $80. Divide by the percentage that's left, not by the discount.
Percent vs. percentage points
If a rate moves from 4% to 5%, it rose by 1 percentage point, but by 25 percent (1 is 25% of 4). News reports and loan offers often mix these up, so check which one is meant.
Mental math shortcuts
- 10%: move the decimal point one place left. 10% of 340 is 34.
- 5%: half of 10%. 5% of 340 is 17.
- Swap the order: X% of Y equals Y% of X. 8% of 50 is the same as 50% of 8, which is 4.