Percent error: keep the size and direction of the error separate
Compare a reading with a reference value without confusing absolute percent error with a signed change.
Method
An error compares an observed result with a stated reference for the same quantity. First express both in the same unit. Subtract the reference from the observation to keep the direction: a negative difference is below the reference, and a positive difference is above it. The reference itself may have uncertainty, so it is not automatically an exact truth.
The Percent error calculator reports the magnitude: the absolute difference divided by the absolute reference value, multiplied by 100. This removes the sign. State which convention you use when reporting an error; a signed relative difference and an absolute percent error answer different questions. The calculator expects a positive reference magnitude.
- Reference value200 g
- Signed differences194 − 200 = −6 g; 206 − 200 = +6 g
- Percent error magnitude6 ÷ 200 × 100 = 3%
Compare a reading with a reference value without confusing absolute percent error with a signed change.
Worked example
Against a 200 g reference, a reading of 194 g differs by −6 g. The magnitude of its error is 6 g and its percent error is 3%. A reading of 206 g differs by +6 g but also has 3% absolute percent error. Equal magnitudes therefore do not mean the readings are on the same side of the reference.
Enter observed value 194 and reference 200 in Percent error to check the 6 g and 3% results. Percentage change from 200 to 194 gives −3%, retaining direction for that positive base. If the reference is zero, percentage error is undefined because division by zero is required. Report the difference in the original unit instead, and do not silently substitute one as the denominator.
194 − 200 = −6 g
|194 − 200| ÷ 200 × 100 = 3%
206 − 200 = +6 g
|206 − 200| ÷ 200 × 100 = 3%
- Reading: 194 g
- 3 %Below the reference (−6 g)
- Reading: 206 g
- 3 %Above the reference (+6 g)
The reference is 200 g. The two readings have equal error magnitudes but opposite directions.
Checks and limits
A small error for one reading does not establish repeatability or explain why a difference occurred. Repeated measurements, instrument limitations and reference uncertainty need separate assessment. Do not interpret 3% error as a confidence interval or a probability that a reading is wrong. Choose a meaningful reference and reporting precision appropriate to the measurement.
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Source: NIST