Percent error versus measurement uncertainty
Percent error expresses the magnitude of the difference between an observed value and a reference value relative to the reference. The absolute-value convention makes the reported percentage nonnegative.
Percent error is not measurement uncertainty. Uncertainty describes quantified doubt or dispersion associated with a measurement result and requires additional data and a defined evaluation method.
How to calculate percent error
- Choose a valid reference: Use an independently justified nonzero reference in the same unit as the observation.
- Enter the observation: Preserve the sign and unit of the experimental value.
- Calculate: Review signed difference, absolute difference, and absolute percent error.
- Report context: State the reference source, units, uncertainty, and rounding separately where relevant.
Formula and variables
The reference must be nonzero. The calculator also reports the signed and absolute differences in the original input unit.
absolute percent error = |xobs − xref|/|xref| × 100%- xobs — Observed value
- Experimental or measured result (shared unit)
- xref — Reference value
- Accepted, assigned, or comparison value (same as xobs)
- xobs − xref — Signed difference
- Direction and magnitude of deviation (input unit)
Measured gravitational acceleration
An experiment gives 9.50 m/s² against a reference of 9.81 m/s².
- Observed
- 9.50 m/s²
- Reference
- 9.81 m/s²
- difference = 9.50 − 9.81 = −0.31 m/s²
- percent error = 0.31/9.81 × 100%
Result: Absolute percent error is approximately 3.16%.
The negative signed difference shows the observation is below the reference; the absolute percentage reports magnitude only.
Understanding your results
A small percent error is not a complete quality statement
Interpretation depends on reference quality, measurement uncertainty, repeatability, method bias, and fitness-for-purpose requirements.
- Signed difference shows direction.
- Absolute difference retains the original unit.
- Percent error is undefined for a zero reference under this formula.
- A single comparison does not estimate precision or uncertainty.
Assumptions
- Observed and reference values describe the same quantity in the same unit.
- The reference is nonzero and appropriate for comparison.
- Absolute percent error is the desired convention.
Limitations
- Does not calculate standard deviation, confidence intervals, propagated uncertainty, relative standard deviation, or statistical significance.
- Does not establish traceability or validate the reference value.
- Can be unstable when the reference is close to zero.
Common mistakes
- Dividing by the observed value instead of the defined reference.
- Dropping the reference sign without using the absolute denominator consistently.
- Calling percent error measurement uncertainty.
- Comparing values in different units.
Practical use cases
Laboratory exercises
Compare one experimental result with a stated accepted value.
Method checks
Report deviation magnitude alongside—not instead of—uncertainty and repeatability evidence.
Frequently asked questions
Can percent error be negative?
Signed percentage difference can be negative, but this calculator uses the common absolute percent-error convention.
Why can’t the accepted value be zero?
The formula divides by the reference magnitude, so a zero reference makes the percentage undefined.
Does this calculate uncertainty?
No. Measurement uncertainty requires a separate evaluation of sources and dispersion; use Error Propagation only when its assumptions fit.
Sources and review
- PERCERR — NIST Dataplot. Accessed 2026-07-13.
- Metrological Traceability: Frequently Asked Questions and NIST Policy — National Institute of Standards and Technology. Accessed 2026-07-13.
Reviewed 2026-07-13.