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.