Percentage Change Calculator
See how much a value went up or down, in percent.
Good to know. Up 50%, then down 50%, is not back where you started. It’s 25% down.
How it works
In plain words
Subtract the old value from the new one, divide by the old value, and multiply by 100. A positive answer is an increase; a negative one is a decrease.
The formula
change = (new − old) ÷ |old| × 100
Worked example
From 80 to 100: the difference is 20, and 20 ÷ 80 × 100 = 25%. That is an increase.
Sources
No outside data or rates: this is plain arithmetic.
8 automated tests check its answers on every change.
About the percentage change calculator
Percentage change tells you how big a change is compared with where you started. A price rising from 80 to 100 is a 20-unit rise, but what matters is that it is 25% more than before. The same 20-unit rise on a 1,000 price would be only 2%.
The starting value is always the reference. That is why changes are not symmetrical: going from 80 to 100 is +25%, but going back from 100 to 80 is −20%. Both are correct, because they are measured from different starting points. This trips up a lot of people when comparing a fall and a recovery, for example in share prices.
If the old value is negative, we divide by its absolute value so that a move upwards is still shown as a positive change. This is the convention used in most finance and statistics textbooks, but percentage changes from negative numbers can still be confusing, so the plain difference is shown too.
A change from zero cannot be expressed as a percentage, since any amount is infinitely larger than nothing. In that case, the difference itself is the useful number.
Questions people ask
What is the formula for percentage change?
(new − old) ÷ old × 100. From 80 to 100 that is 20 ÷ 80 × 100 = 25%.
Why is a 20% fall not undone by a 20% rise?
Because the second change starts from a smaller number. 100 falls 20% to 80, but 80 needs to rise 25% to get back to 100.
What is the difference between percentage change and percentage points?
Percentage points measure the gap between two percentages (5% to 7% is 2 points). Percentage change measures relative growth (5% to 7% is a 40% increase).
Can I calculate a change from 0?
No. Any change from zero is infinitely large as a percentage, so only the plain difference makes sense.