Percentage Calculator
- What is X% of Y — discounts, commission, tips. 20% of 250 is 50.
- X is what % of Y — a share of the total. 50 is 20% of 250.
- Increase Y by X% — adding to a value. 250 plus 20% becomes 300.
- Decrease Y by X% — applying a discount. 250 minus 20% becomes 200.
- Change from X to Y — how much moved between two values, as a percentage.
This is the most common mistake with percentages. Raising a value by 20% and then cutting 20% does not return the original.
Starting at 100: the increase gives 120. The 20% cut applies to 120, not to 100, so it removes 24 and lands at 96.
The reason is that the base changes between operations. A product that rose 50% must fall 33.3% to return to its previous price, not 50%.
If a rate moves from 5% to 7%, it rose by 2 percentage points — but the percentage change is 40%.
Confusing the two shows up constantly in reporting on interest rates, inflation and polling, and it changes the interpretation entirely.
Use percentage change to express the relative size of a move; use percentage points when both values are already percentages.
Frequently asked questions
No. The base changes between operations. Starting at 100 you end at 96, because the discount applies to 120 rather than 100.
Moving from 5% to 7% is a 2 percentage point difference but a 40% change. Percentage points compare percentages to each other; percentage change measures relative movement.
Divide the final price by the complement of the discount. An item at 80 with 20% off originally cost 100, because 80 divided by 0.8 is 100.
Do not add the percentages. Apply them one at a time: 10% then another 10% gives 19% total, not 20%.