Three common percentage problems
"Percent" means "per hundred," so 25% is 25/100 or 0.25. Almost every everyday percentage question falls into one of three types, and this calculator solves all three at once.
1. What is X% of Y?
Multiply Y by X divided by 100. For example, 15% of 200 = 0.15 × 200 = 30. Use this for discounts, commissions, tips and tax.
2. X is what percent of Y?
Divide X by Y and multiply by 100. For example, 30 out of 120 = 30 ÷ 120 × 100 = 25%. Use this for test scores, budget shares or survey results.
3. Percentage change from X to Y
Subtract the old value from the new value, divide by the old value, and multiply by 100: (new − old) ÷ |old| × 100. Going from 50 to 65 is a 30% increase; going from 65 to 50 is a 23.08% decrease. Notice those aren't symmetric: the base changes depending on direction.
Common mistakes
- Percentage points vs. percent: if a rate rises from 4% to 5%, that's a 1 percentage point increase but a 25% relative increase.
- Stacking percentages: a 50% gain followed by a 50% loss doesn't return you to the start. $100 → $150 → $75.
- Reversing a discount: if a price after 20% off is $80, the original was $80 ÷ 0.8 = $100, not $80 × 1.2 = $96.
Where percentages show up
Percentages are everywhere: interest rates, inflation, grades, nutrition labels, sales and investment returns. Being comfortable converting between fractions, decimals and percents makes comparing prices and offers far easier. For shopping specifically, try our discount and sales tax calculators.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. 20% of 50 = 50 × 20 / 100 = 10.
How do I calculate percentage increase?
Subtract the original from the new value, divide by the original, then multiply by 100.
What is the difference between percent and percentage points?
Percentage points measure the simple difference between two percentages; percent change measures the relative difference.