About the Percent Error Calculator
Percent error measures how far a measured or estimated value is from the true value, expressed as a percentage of the true value. It is the standard way to report accuracy in laboratory work, engineering, and forecasting, because a percentage is comparable across quantities of any size.
The formula
Percent error = |observed − true| / |true| · 100The observed value is what you measured or predicted; the true value is the accepted or actual figure. The absolute value makes the error non-negative, so it describes magnitude rather than direction.
How to use this calculator
- 1Enter your Observed Value. The field starts at
10, which you can overwrite. - 2Enter your True Value. The field starts at
12, which you can overwrite. - 3Read the result straight away — it recalculates as you type, so there is no button to press. Use Share to copy a link that reopens the page with your exact numbers filled in.
Worked example
| Input | Value |
|---|---|
| Observed Value | 10 |
| True Value | 12 |
Result
16.67%
Those are the values the page loads with, so you can reproduce this result yourself and then change one field at a time to see what drives the outcome.
Understanding your result
Dividing by the true value is what makes the measure meaningful. An absolute error of 2 units is trivial when measuring 1,000 and severe when measuring 3, and only the relative form captures that. This is why percent error, rather than raw difference, is what appears in lab reports.
Percent error describes accuracy — closeness to the truth — and says nothing about precision, which is the repeatability of your measurements. An instrument can be highly precise and consistently wrong, which is exactly what a systematic calibration error looks like. Random error scatters results around the true value; systematic error shifts them all in one direction.
Things worth knowing
- Percent error is undefined when the true value is zero, because dividing by zero has no meaning. Use absolute error in that case.
- Where direction matters, drop the absolute value: a signed relative error shows whether you over- or under-estimated.
- What counts as acceptable depends entirely on context. Under 5 percent is often fine in a teaching lab and far too loose in precision engineering.
- Consistent error in one direction points to a systematic problem — a miscalibrated instrument or a flawed method — not to bad luck.
- Do not confuse percent error with percent difference, which compares two measurements to their own average when no true value exists.
Frequently asked questions
What counts as a good percent error?+
It depends on the field. Introductory laboratory work often accepts under 5 or 10 percent, while machining and metrology may require a fraction of a percent. The tolerance is set by the application, not by a universal rule.
Can percent error be negative?+
Not in the standard definition, which uses absolute value. If you want to show whether you overestimated or underestimated, omit the absolute value and report a signed relative error.
What is the difference between accuracy and precision?+
Accuracy is closeness to the true value, which is what percent error measures. Precision is how tightly repeated measurements agree with each other. A measurement can be precise but inaccurate if the instrument is miscalibrated.
What if the true value is zero?+
Percent error cannot be calculated, since it would require dividing by zero. Report the absolute error instead, or use a different reference value appropriate to the measurement.