Percentage difference vs. percentage change — they are not the same thing
This distinction is the whole reason this page exists. Percentage change is directional: it measures how much a value grew or shrank relative to where it started. Going from 40 to 60 is a +50% change, but going from 60 to 40 is a −33.3% change — same two numbers, different answers, because the baseline changed. Percentage difference is symmetric: it measures the gap between two values relative to their average, so 40 vs. 60 is a 40% difference no matter which one you type first. Use percentage change when one value is a genuine "before" (last year's revenue, the original price). Use percentage difference when the two values are peers and neither deserves to be the baseline (two vendors' quotes, two thermometers' readings).
The formula
a and b are your two values; |a − b| is the absolute gap between them, and (a + b) ÷ 2 is their average. Because the denominator treats both values equally, swapping a and b changes nothing.
Worked example
Compare 40 and 60:
Gap = |40 − 60| = 20. Average = (40 + 60) ÷ 2 = 50. Percentage difference = 20 ÷ 50 × 100 = 40%.
Contrast with percentage change on the same numbers: 40 → 60 is +50%, while 60 → 40 is −33.3%. Three different percentages from one pair of numbers — which is exactly why you should name the one you're using.
A note on misuse
Headlines and reports mix these up constantly — "50% difference between the two plans" often turns out to mean a 50% change from the cheaper one, which is only a 40% difference by the symmetric measure. When you quote a percentage comparing two numbers, say which formula you used and, ideally, give the raw values too. Also know the formula's limits: with values of opposite signs the average can hit zero and the result becomes undefined or meaningless — percentage difference is built for comparing two positive quantities.