How percent change works
Percent change measures the difference relative to the original value:
% change = (new − original) ÷ |original| × 100
The absolute value in the denominator keeps the sign sensible when the original is negative (a loss from −50 to −30 is a 40% decrease, not −40%). A positive result is an increase, a negative result a decrease. Note the asymmetry: falling 50% to 25 is −50%, but climbing back from 25 to 50 is +100% — you need a 100% gain to recover a 50% loss. This is why "down 50%, up 50%" is never back to the start.
Worked example
A price rises from $80 to $92: change = (92 − 80) ÷ 80 × 100 = +15%, a $12 increase, and 92 ÷ 80 = 1.15× the original. Read in reverse (92 → 80) the same change is −13.04% — different number, same two prices, which is exactly why financial reports state the base period explicitly.
Percent change, percent of, and percent difference
Do not confuse these three. Percent change has a direction (old → new) and is the one above. Percent of asks what portion one number is of another (50% of 200 = 100). Percent difference compares two values with no direction, always using the mean as the base — used when the two values are peers rather than before-and-after (e.g. comparing two test scores). Discounts are a special case: a 20% discount off $80 means you pay $64, and the price drop looks like 20% while the "reverse" change from 64 to 80 reads as +25%.