Percentage change calculator
Enter a starting value and a final value: get the percentage increase or decrease, the multiplier and the change that would bring you back.
Increase of
+25%
from 80 to 100
- Difference
- +20
- Multiplier
- 1.25
- Change needed to get back
- -20%
How we calculated it
Percentage change = (final − start) ÷ start × 100
(100 − 80) ÷ 80 × 100 = 25%
A price goes from 80 to 100, a salary from 2,400 to 2,520, a website from 12,000 to 9,000 visits a month. In each case the useful number is not the difference but the percentage change, because it can be compared from one situation to another.
This page computes it in both directions and adds two figures that are often overlooked: the multiplier, which lets you chain several changes, and the change needed to return to the starting point, which is never the same percentage in reverse.
How to use it
- Enter the starting valueThe value before the change: last year’s price, the old salary, the previous month’s figure. It cannot be zero, since no change can be measured against nothing.
- Enter the final valueThe value after the change. If it is lower than the start, the result is a decrease and carries a minus sign.
- Read the result and the formulaThe percentage change, the difference, the multiplier and the change needed to get back update as you type.
The formula
Percentage change = (final value − starting value) ÷ starting value × 100. From 80 to 100, that gives (100 − 80) ÷ 80 × 100 = +25%. The base is always the starting value: the same 20-point gap measured against 100 would only be 20%.
The multiplier is final ÷ start, here 1.25. A decrease of 25% corresponds to a multiplier of 0.75. Multipliers can be chained: a rise of 10% followed by another of 10% gives 1.1 × 1.1 = 1.21, so +21% in total, not +20%.
Why going back is not the same percentage
After a 25% increase, from 80 to 100, a 25% decrease does not bring you back to 80 but to 75. To return to 80 you need to remove 20%, because the base has grown. This is why the page shows the change needed to get back.
From 120 to 90 is a fall of 25%. Getting back from 90 to 120 requires a rise of 33.33%.
The gap widens with the size of the change: a fall of 50% has to be followed by a rise of 100% to recover, which is why heavy losses on an investment take so long to make up.
Percentage change or percentage points?
When the values are themselves percentages, two answers are possible. An interest rate that goes from 4% to 5% rises by one percentage point, but by 25% in relative terms. Both statements are correct; confusing them is the most common error in reporting on rates. For gaps between rates, the page’s result is the relative change.