Tutorials
How to Calculate Percentages Without Mistakes
Most percentage problems are one of three questions. Once you know which one you are answering, the arithmetic is short. You can check each example with the Percentage Calculator.
1. What is X percent of Y?
Multiply Y by X and divide by 100. So 15% of 80 is 80 × 15 ÷ 100 = 12.
2. X is what percent of Y?
Divide X by Y and multiply by 100. So 12 is 12 ÷ 80 × 100 = 15% of 80.
3. What is the percentage change from A to B?
Subtract A from B, divide by A, multiply by 100. From 80 to 100 the change is (100 − 80) ÷ 80 × 100 = +25%. Going back from 100 to 80 is (80 − 100) ÷ 100 × 100 = −20%. The numbers are the same but the percentages differ, because each change is measured against a different starting point. If the starting value is 0, the percentage change is undefined.
Common mistakes
- Stacking discounts. 20% off followed by 10% off is not 30% off. A price of 100 becomes 80, then 72, which is 28% off in total.
- Percent versus percentage points. If a rate rises from 4% to 5%, that is 1 percentage point, which is a 25% increase in the rate.
- Using the wrong base. Always ask what the percentage is of. “20% more” refers to the original amount, not the new one.
Quick check
If your answer to “X percent of Y” is larger than Y while X is below 100, something went wrong. For one-off arithmetic, the Basic Calculator is enough.