Percentage Error Calculator

PERCENTAGE ERROR

0.306%

|9.78 − 9.81| ÷ |9.81| × 100. The measurement sits 0.03 m/s² below the accepted value, which is 0.306% of it.

Put the measured value underneath instead and you get 0.307%. That is not a small discrepancy — it is the answer multiplied by 1.0031, which is exactly the accepted value divided by the measured one. Percentage error is asymmetric by design, because the accepted value is the reference and the measurement is what is being judged against it. Swapping them asks a different question and gets a different number.

Percentage difference comes out higher here, at 0.306%. It divides by the mean of the two values rather than by one of them, which makes it symmetric — swap the inputs and it does not move. That is the entire reason it exists. It reads higher than percentage error whenever the measurement undershoots, because the mean is then smaller than the accepted value alone. Use it when neither number has a claim to being correct — two instruments disagreeing, say.

On signs and significant figures. The absolute-value bars are the usual convention in school and laboratory work, which is why the headline figure is positive. The signed version — -0.306% here — keeps the direction, and a systematic underestimate is often the more useful thing to report, because a bias that always points one way suggests a fault in the method rather than noise. As for precision: a percentage error cannot be more precise than the measurement behind it, so quoting it to five decimals when the reading had three significant figures is inventing certainty.