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 the difference divided by the starting value, times 100. Going from 80 to 100 is a 25% increase; going back from 100 to 80 is a 20% decrease. The base changes, so the percentages differ.
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.
Questions
(new − old) ÷ old × 100. The old value is always the base.