Percent Increase & Decrease

Percent change compares how much something moved to where it started.

Price goes from $40 to $50. The change is $10, and you divide by the original 40: 10/40 = 0.25, so a 25% increase.

The denominator is always the original value. That is the whole thing, and it is where nearly every mistake happens.

Note that increases and decreases do not undo each other. Up 50% then down 50% does not return you to the start: 100 → 150 → 75.

Percent change is defined relative to the initial value:

percent change = (new − old)/old × 100%

The asymmetry is structural, not a quirk. Going from 40 to 50 is a 25% increase, but 50 to 40 is a 20% decrease, because the base changed. Any claim about a percent change is meaningless without knowing its base, which is what makes the statistic so easy to misuse in reporting.

In multiplier form, an increase of p% is multiplication by (1 + p/100) and a decrease by (1 − p/100). Successive changes compose by multiplication, so +50% then −50% gives 1.5 × 0.5 = 0.75, a net 25% loss. Reversing a p% increase requires a decrease of p/(100+p), not p.

Distinguish percent change from percentage points: a rate moving from 4% to 6% is a rise of 2 percentage points but a 50% increase.