Percentage formulas
| Question | Formula | Example |
|---|---|---|
| X% of Y | X × Y ÷ 100 | 15% of 240 = 36 |
| X is what % of Y | X ÷ Y × 100 | 45 is 25% of 180 |
| % change | (Y − X) ÷ X × 100 | 1,250 → 1,400 = +12% |
Percent vs. percentage points
If a rate rises from 4% to 5%, it went up by one percentage point, but by 25% in relative terms. News reports about interest rates and polls usually mean percentage points.
Everyday examples
- Raises: a raise from $52,000 to $54,600 is a 5% increase, because $2,600 ÷ $52,000 = 0.05.
- Test scores: 42 correct out of 50 is 84%, because 42 ÷ 50 × 100 = 84.
- Prices: a $1,250 laptop that now costs $1,400 went up 12%.
- Budgets: spending $1,800 of a $4,500 monthly income on rent is 40% of income.
Percent change vs. percent difference
Percent change measures movement from an old value to a new one, so the starting number matters. Percent difference compares two values with no before or after. It divides the gap by their average. Use percent change for prices over time, and percent difference for comparing two stores or two products.
Frequently asked questions
Is a 50% increase undone by a 50% decrease?
No. 100 increased by 50% is 150, and 150 decreased by 50% is 75. The second change applies to a larger starting number.
How do I add a percentage to a number?
Multiply by 1 plus the percentage as a decimal. Adding 8% to 250 is 250 × 1.08 = 270.
How do I find the original number before a percentage was added?
Divide by 1 plus the percentage. If $270 includes an 8% increase, the original was 270 ÷ 1.08 = $250.