Percentage change calculator
Eighty rising to a hundred is a 25% increase. A hundred falling to eighty is a 20% decrease. The same absolute change gives different percentages because the base differs, and it is why a stock that drops 50% needs a 100% rise to recover. Percentage change is never symmetric, and treating it as though it were is one of the most common numerical errors in reporting.
Percentage change is (new − old) ÷ old × 100: the difference divided by the value you started from. Going from 80 to 100 is a 25% increase; going back from 100 to 80 is a 20% decrease, because the base is now the larger number. An increase has no upper limit, while a decrease can never pass −100%, since nothing falls below zero.
How to calculate percentage change
Percentage change and percentage point change are different things and are constantly confused. If an interest rate goes from 4% to 6%, that is a two percentage point rise and a fifty per cent increase: both statements are true and they describe the same event very differently. Where the underlying quantity is itself a percentage, saying "points" rather than "per cent" removes the ambiguity entirely. Percentage difference is a third measure again, and this tool deliberately does not report it: it divides by the average of the two values rather than by the first, so 80 and 100 differ by 22.2% whichever order you write them in. That symmetry is only appropriate when neither figure is the starting point. A before-and-after comparison always has one, and that one is the base.
What people use it for
- Reporting a year-on-year movement with the base stated explicitly
- Working out how far a price has to rise to undo the fall it took
- Checking a growth figure in a press release against the two numbers
- Comparing two changes that were measured from different starting values
- Deciding whether a movement should be quoted in points or in per cent
Questions
(new − old) ÷ old × 100. The old value is always the base.
Because the base differs. Going 80 to 100 divides by 80; going 100 to 80 divides by 100.
The arithmetic difference between two percentages. From 4% to 6% is two points and a 50% increase.
Yes, for increases. A decrease cannot go below −100%, since a value cannot fall further than to zero.
The change is undefined; you cannot divide by zero. Report it as an absolute increase instead.
No. Percentage difference divides by the average of the two values, so 80 and 100 differ by 22.2% read either way round. This tool divides by the first value, which is the right choice whenever one of them is the before and the other the after.
By more than it fell. Down 20% needs 25% back, down 50% needs 100%, down 80% needs 400%. The multiplier row is the quickest way to see it: recovery is one divided by the multiplier.