Percentage error vs percent change: not the same formula

Three formulas in this family look nearly identical — a subtraction, a division, a multiplication by 100 — and get used interchangeably in casual writing. They are not interchangeable. Percentage error is a science and engineering term: how far a measurement fell from a known, accepted value. Percent change is a finance and stats term: how much a value moved from an earlier observation to a later one, with no claim that either value is “correct.” Mixing them up produces numbers that are arithmetically fine but answer the wrong question.

Percentage error: measurement against a known truth

Percentage error appears in labs, manufacturing tolerances, and instrument calibration. The formula:

% error = |measured − true| ÷ |true| × 100

The denominator is always the accepted or true value — the one you're not questioning, whether that's a physical constant, a certified reference weight, or a calibration standard. If a scale reads 9.7 g for a certified 10.0 g weight, the percentage error is |9.7 − 10.0| ÷ 10.0 × 100 = 3%. The scale's reading is wrong by 3% of the true weight — not 3% of its own reading.

Percent change: observation against an earlier observation

Percent change appears when tracking a value over time — prices, populations, temperatures, account balances. Neither number is more “correct”; one is simply earlier.

% change = (new − old) ÷ old × 100

If a stock moves from $9.70 to $9.80, that's (9.80 − 9.70) ÷ 9.70 × 100 ≈ +1.03%. The sign is kept — a drop from $9.80 to $9.70 is −1.02%, not the same magnitude reversed, because the denominator changes with which value came first. This asymmetry is covered in more depth in our guide to percent change vs percent difference.

Why picking the wrong one distorts the story

Suppose a thermometer reads 21°C in a room that's actually 20°C (a certified reference reads 20°C). If you report this as “a 4.76% change” using the percent-change formula with 20 as the base, you've accidentally reported the correct percentage error — but called it the wrong thing, and the label matters when someone else tries to reproduce or audit the number. In manufacturing tolerance specs, using percent change instead of percentage error against a known true dimension would mean the “old” value is whatever the last measurement happened to be, not the engineering spec — a moving target that makes tolerance checks meaningless.

A worked example: instrument calibration

A pressure gauge is checked against a certified 100.0 psi reference and reads 97.5 psi.

The gauge has a 2.5% error against the reference. If that same gauge later reads 98.0 psi on a re-check, the percent change between the two readings — 97.5 to 98.0 — is a separate calculation, +0.51%, describing drift between two of the gauge's own readings rather than its accuracy against the reference.