Percentage change

What it's for

Two numbers, before and after, and the question is how much it changed: the bill compared with last year, the salary after the raise, a site's visits, your weight, the price of petrol. A percentage is the way to compare changes in quantities of different sizes: ten euros more on fifty is a lot, ten euros more on two thousand goes unnoticed, and only the percentage says so.

The denominator is the starting value

Change = (final value − starting value) ÷ starting value × 100. The number you divide by is always the starting one, and that's the commonest mistake: from 100 to 120 is +20%, but from 120 to 100 is −16.7%, not −20%. The two changes are equal in euros and different in percentage, because they start from different bases.

From this comes a consequence that always surprises: to recover a 50% fall you need a rise of 100%, not 50. It's why a loss on the stock market hurts more than it looks.

Percent and percentage points are not the same thing

If a rate goes from 4% to 6%, it grew by two percentage points, but it grew by 50 per cent. They're two true sentences saying very different things, and newspaper headlines swap them constantly: whenever percentages of percentages are involved (rates, unemployment, market share) it's worth asking which of the two you're reading.

Nearby tools

If instead you have the value and the percentage and want the result, the page is Increase or reduce by a %; if you have two prices and want the discount, Discount percentage. To compare two sums far apart in time, where the value of money changes too, there is Inflation calculator.