Understanding percentages
A percentage expresses a number as a fraction of 100. The word comes from the Latin "per centum", meaning "by the hundred". Percentages are used everywhere: discounts, taxes, interest rates, test scores and statistics.
The three main formulas
- X% of Y: multiply Y by X and divide by 100.
- X is what percent of Y: divide X by Y and multiply by 100.
- Percentage change: (new value − old value) ÷ old value × 100.
Practical examples
A jacket costs $80 and is on sale for 25% off. The discount is 25% of 80, which equals $20, so the sale price is $60. If a salary rises from $2,000 to $2,200, the increase is 200 ÷ 2000 × 100 = 10%.
Percentage points vs percent
If an interest rate goes from 4% to 6%, it rises by 2 percentage points, but that is a 50% increase in the rate itself. Keeping this difference clear avoids common misunderstandings in news and finance.
Frequently asked questions
How do I calculate a discount?
Multiply the original price by the discount percentage and divide by 100, then subtract the result from the original price.
Why can't I calculate change from zero?
Percentage change divides by the starting value, and dividing by zero is undefined.
Can percentages exceed 100%?
Yes. For example, a value that doubles has increased by 100%, and one that triples has increased by 200%.