Percentages, three ways.
What is X% of Y, what percentage one number is of another, and the change between two figures.
Plain arithmetic — no assumptions, no data sources, no rounding beyond display.
| 15% of $2,400 | $360.00 |
| 45 as a share of 180 | 25% |
| Change from $1,200 to $1,560 | +30% |
| Absolute change | $360.00 |
Percentage change is undefined when the starting value is zero, and a percentage-point difference is not the same as a percentage change.
Three questions, and the one everyone gets backwards
Almost every percentage question in daily life is one of three: a share of an amount (a 15% tip on $2,400), a ratio expressed as a percentage (45 out of 180), or a change between two numbers (from $1,200 to $1,560). This page answers all three at once so you can read the one you need without reframing the problem.
The third is where the mistakes live, because percentage change is not symmetric. A price that rises 25% and then falls 25% does not return to where it started — it lands 6% lower, since the decrease applies to the larger number. The same asymmetry explains why an investment that loses 50% needs a 100% gain to recover.
A percentage point is also not a percent. When a rate moves from 4% to 5%, that is one percentage point, but a 25% increase. Reporting the two interchangeably is one of the most common errors in coverage of interest rates, tax rates and poll results — and the distinction usually favours whoever is choosing which figure to quote.
For discounts, the order of operations matters: stacked discounts multiply rather than add, so 20% off then a further 10% off is 28% off, not 30%. And when tax is applied after a discount, applying them in the other order gives the same total — a rare case where the sequence genuinely does not matter.
Common questions
How do I work out a tip quickly?
Move the decimal one place left for 10%, then halve that for 5%. Add them for 15%, double the 10% for 20%.
Why does a 25% rise then a 25% fall not cancel out?
The fall applies to a bigger number than the rise did. $100 rises to $125, then falls by $31.25 to $93.75.
What is the difference between percent and percentage point?
A move from 4% to 5% is one percentage point and a 25% increase. Both are correct; they describe different things.
Sources & method
Share: percentage divided by 100, multiplied by the amount.
Ratio: the first number divided by the second, multiplied by 100.
Change: the difference divided by the original value, multiplied by 100 — undefined when the original is zero.
The Index
Every calculator is built the same way: real 2026 figures, method printed at the foot of the page.