Percent Error and Measurement Uncertainty

Error and uncertainty

Percent error measures how far an observation is from a known reference. Divide the absolute difference by the absolute reference and multiply by 100. A zero reference makes this ratio undefined. A measurement of 102 against a reference of 100 has signed error 2 and absolute percent error 2. Uncertainty describes the spread of values attributed to a result and is not the error itself.

Combining components

Enter up to five uncorrelated standard uncertainties. Leave unused components at zero. Multiply each uncertainty by its sensitivity coefficient, square these contributions, add them and take the square root. Contributions of 3 and 4 therefore combine to 5. A coverage factor of 2 gives expanded uncertainty 10. This factor alone does not establish 95 percent confidence. Correlation, effective degrees of freedom and distribution selection are outside this calculation.

Combine contributions in the output unit

Take two uncorrelated standard uncertainties 0.2 and 0.3, with sensitivity coefficients 2 and 1 respectively. Output contributions are 2 × 0.2 = 0.4 and 1 × 0.3 = 0.3. Combined standard uncertainty is √(0.4² + 0.3²) = 0.5. Choosing example coverage factor 2 gives expanded uncertainty 1. Enter zero for unused components. This factor is not a recommendation for a confidence level.

Input uncertainties may use different units, but all contributions must share the output unit after multiplication by sensitivities. Do not choose coefficients from magnitude alone without their units. A negative sensitivity does not produce negative uncertainty in this uncorrelated model because its contribution is squared.

Correcting a known measurement bias is different from enlarging uncertainty. In the error mode, signed difference identifies the side of the reference and absolute percentage gives relative deviation. Do not equate that percentage with uncertainty. Shared calibration or other input dependence can require covariance terms. This tool does not resolve that dependence. Document the measurement model, components, units and chosen coverage factor with the result.

Frequently asked questions

How do you calculate percent error from an expected value?

In this example, dividing the absolute difference by the absolute reference gives 4 percent error for a measurement of 96 against a reference of 100. This expresses deviation from the reference, not measurement uncertainty, and the percentage is undefined when the reference is zero.

Calculate with these values