Percent Error Calculator
Use this percent error calculator to compare a measured (observed) value with the true (accepted) value. Get instant absolute and signed percent error, absolute error and relative error, plus a clear step-by-step explanation for lab reports, QA documentation and statistics homework.
Calculate percent error
Reference value from standards, specifications or high-accuracy instruments.
Value measured in your experiment, test or instrument reading.
Supports both dot and comma as decimal separator.
Percent error formula
Percent error tells you how far a measured value is from the true or accepted value, relative to that true value. The standard definition uses an absolute value so that the result is always non-negative:
\( \text{percent error} = \dfrac{\left| V_{\text{obs}} - V_{\text{true}} \right|}{\left| V_{\text{true}} \right|} \times 100\% \)
- \( V_{\text{true}} \) = true, accepted or reference value
- \( V_{\text{obs}} \) = observed, measured or experimental value
In some contexts (for example, to show whether your measurement is higher or lower than the reference), a signed percent error is used:
\( \text{signed percent error} = \dfrac{V_{\text{obs}} - V_{\text{true}}}{V_{\text{true}}} \times 100\% \)
Worked example
Suppose the true density of a material is \( 7.85 \,\text{g/cm}^3 \), and your lab measurement gives \( 7.62 \,\text{g/cm}^3 \). What is the percent error?
- Compute the absolute error: \( |7.62 - 7.85| = 0.23 \,\text{g/cm}^3 \).
- Compute the relative error: \( \dfrac{0.23}{7.85} \approx 0.0293 \).
- Convert to percent: \( 0.0293 \times 100\% \approx 2.93\% \).
So your measurement has a percent error of about 2.93% relative to the accepted density.
Percent error vs percent difference vs percent uncertainty
Several related quantities are easy to confuse with percent error:
- Percent error compares a measured value to a known true or accepted value, dividing by the true value.
- Percent difference compares two measured values of equal status and divides by their average. It is used when there is no clear “true” value.
- Percent uncertainty expresses the uncertainty of a measurement (for example, a standard deviation or confidence interval) as a percentage of the measured value.
In calibration, physics and chemistry labs, and quality control, percent error is usually the relevant metric because you compare your result to a reference standard, specification or certified value.
When is a percent error acceptable?
What constitutes a “good” percent error depends entirely on the application:
- In an introductory teaching lab, percent errors below about 5% are often considered very good, and below 10% can still be acceptable depending on the experiment.
- In industrial metrology or calibration labs, acceptable limits are usually much tighter and defined by standards, contractual tolerances or regulatory requirements.
- In statistics and data science, percent error may be one of several accuracy metrics (alongside MAE, RMSE, MAPE, etc.) used to evaluate models or instruments.
Rather than treating percent error as “good” or “bad” in isolation, always compare it with the required tolerance for your specific measurement task.
Percent error – frequently asked questions
Formula (LaTeX) + variables + units
','\
\( \text{percent error} = \dfrac{\left| V_{\text{obs}} - V_{\text{true}} \right|}{\left| V_{\text{true}} \right|} \times 100\% \) \( V_{\text{true}} \) = true, accepted or reference value \( V_{\text{obs}} \) = observed, measured or experimental value
\( \text{signed percent error} = \dfrac{V_{\text{obs}} - V_{\text{true}}}{V_{\text{true}}} \times 100\% \)
- No variables provided in audit spec.
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.