Three questions, one calculator
Almost every percentage problem is one of three:
- X% of Y — a discount, a tax, a tip, a commission.
- X is what % of Y — a share, a conversion rate, a completion figure.
- Change from X to Y — growth, a price rise, a drop in traffic.
They use different formulas and get mixed up constantly, so each has its own mode here rather than one box that guesses.
The reversal trap
Percentage changes do not cancel out, because each is measured against a different base. A 20% discount followed by a 20% markup does not return the original price — it lands 4% below it. The ratio figure in change mode exists for exactly this: it tells you what to multiply by, which is the number that does compose.
Percent versus percentage points
A conversion rate moving from 2% to 3% has risen by one percentage point and by fifty percent. Reporting the second without saying so is the standard way to make a small change sound large. When you compare two percentages, use points; when you compare two amounts, use percent.
Questions
Why is a 50% rise followed by a 50% fall not back where it started?+
Because each percentage is taken of a different base. 100 rises by 50% to 150; 50% of 150 is 75, so you land on 75, not 100. To undo a 50% rise you need a 33.3% fall. This is the single most common percentage mistake in pricing and in reporting.
What is the difference between percent and percentage points?+
If a rate moves from 4% to 6%, that is a rise of two percentage points and a rise of 50 percent. Both are correct and they mean different things. Use points when comparing two percentages, and percent when comparing two quantities.
Can I enter decimals and negative numbers?+
Yes. Decimals work in every field, and the change mode handles negative starting values by measuring against the absolute size of the original, so a move from −200 to −100 reads as a 50% improvement rather than a nonsensical figure.
Why does dividing by zero show a dash?+
Asking what share a number is of zero has no answer, so the tool shows a dash rather than Infinity or NaN. If you meant percentage change from zero, that is also undefined — any increase from nothing is infinite in percentage terms.