The three percentage formulas
What is X% of Y? (X ÷ 100) × YX is what % of Y? (X ÷ Y) × 100% change ((new − old) ÷ old) × 100Worked examples
Discount: 15% of $200 = (15 ÷ 100) × 200 = $30 off, so you pay $170. Scores: 45 marks out of 60 = (45 ÷ 60) × 100 = 75%. Growth: a price rising from $80 to $100 is ((100 − 80) ÷ 80) × 100 = a 25% increase — note it is divided by the old value, not the new one.
Percent vs percentage points
If an interest rate moves from 4% to 5%, that is 1 percentage point higher, but a 25% increase in the rate itself. News reports mix these up constantly; this calculator's third mode always divides by the starting value, which is the correct convention for percentage change.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For example, 20% of 150 = 0.20 × 150 = 30.
How do I find the percentage increase?
Subtract the old value from the new value, divide by the old value, and multiply by 100. Use mode 3 above and it does all three steps.
What is a reverse percentage?
Finding the original price before a percentage was added or removed — for example, the price before 20% tax. Divide the final price by 1.20. A dedicated reverse-percentage tool is on our roadmap.
Why is my percentage change different from a friend's?
Usually because one of you divided by the new value instead of the old one. Percentage change is always measured against where you started.