What this percent error calculator does
The percent error calculator measures how accurate a measurement or estimate is relative to the accepted true value. It shows three things at once: the absolute error (the raw difference, in the same units as your values), the percent error using the standard absolute-value formula, and the signed percent error so you can tell whether your reading came in too high or too low. It's the workhorse number for science labs, engineering checks and quality control.
The formula
Absolute percent error: |observed − true| ÷ |true| × 100%
Signed percent error: (observed − true) ÷ |true| × 100%
Most textbooks present the absolute version because experimental accuracy is usually about size of error, not direction. The signed version is useful when you need to know whether your instrument is biased high or low.
Percent error vs percent difference
Pick the right tool for what you have. Use percent error when one of the two values is an accepted truth — a published constant, a target spec, an expected theoretical result. Use percent difference when you are comparing two measurements with no preferred reference between them, dividing by their average instead of by one of them.
Reading the result
Rough quality bands used in many lab courses:
- Under 5% — very good for a student lab
- 5%–10% — acceptable for introductory work
- 10%–25% — significant deviation; check method and equipment
- Over 25% — likely a systematic issue; re-run the experiment
What counts as "good" depends entirely on the precision required. A 1% error on g (gravity) is normal in a classroom but unacceptable for a national gravity survey.
How to lower percent error
Three big levers, in order of payoff:
- Repeat and average. Random error shrinks like 1/√n with more readings.
- Calibrate. Check your instrument against a known standard before measuring.
- Identify systematic bias. If every reading is off the same way, the cause is your method or hardware, not random noise.
Edge case: true value of zero
If the true value is zero the percent error formula divides by zero, which is undefined. This calculator detects that and shows "Undefined" along with a hint to use absolute error instead. In that situation, absolute error in the original units is the right thing to report.
Use with the other tools
For general percentage maths, see the percentage calculator. For spread and variability in a data set, the standard deviation calculator shows population and sample SD. For simple averaging, the average calculator gives mean, median and mode.