Percent Difference

When neither of two numbers has a better claim to being right (two students' measurements of the same rod, two instruments on the same sample, this month's figure against last month's) percent difference divides the gap by their average, so the answer does not depend on which one you list first. Values of 12 and 10 differ by 2 against an average of 11, giving 2/11 ≈ 18.2%. Compare that with percent change, which uses the earlier value as the base and would report 20% going up but 16.7% coming back down; the symmetric version avoids that asymmetry entirely.

The trap is picking the wrong tool. Percent error when one value is an accepted reference, percent change when there is a genuine before and after, percent difference only when the two are peers. Chemistry labs use it for replicate titrations and typically demand agreement within a few percent before accepting a result. Because both the numerator and denominator move together, the measure is capped: two positive numbers can never differ by more than 200%. Solving backwards is a neat check on a spec: if a duplicate must agree within 20% and one reading is 9, the other may run as high as 9 × 2.2/1.8 = 11.