The formulas
- X% of Y = X ÷ 100 × Y. Example: 15% of 200 is 30.
- X is what % of Y = X ÷ Y × 100. Example: 30 is 15% of 200.
- Percentage change = (new − old) ÷ |old| × 100. Going from 50 to 75 is +50%.
- Increase by X% = Y × (1 + X/100). Decrease = Y × (1 − X/100).
Percent change is not symmetrical
If a price rises 50% and then falls 50%, you do not return to the start: 100 becomes 150 and then 75. A fall of 33.3% is needed to undo a 50% rise. This is why percent change always depends on which number you start from.
Percentage points vs percent
If an interest rate goes from 4% to 5%, it rose by one percentage point but by 25 percent relative to the old rate. News stories often mix these up, so check which one is meant.
Frequently asked questions
How do I calculate a discount?
Use "Decrease Y by X%" - or try the Discount & Sales Tax calculator.
What if the starting value is negative?
Percent change uses the absolute value of the starting number so the direction stays meaningful.
How many decimals are shown?
Up to six, with trailing zeros removed.