Expanded Uncertainty

Expanded uncertainty (U) is the final result of an uncertainty analysis and the value reported on calibration certificates. It is calculated as U = k × u_c, where k is the coverage factor and u_c is the combined standard uncertainty. The expanded uncertainty defines a range (measured value ± U) that is expected to contain the true value with a stated probability, typically 95% when k=2 is used.

Expanded uncertainty is the most practically useful form of uncertainty because it provides a directly interpretable confidence interval. A calibration certificate reporting "10.000 V ± 0.003 V (k=2, 95% confidence)" means there is approximately 95% probability that the true voltage is between 9.997 V and 10.003 V. This information is used for decision-making, TUR calculations, and further uncertainty propagation when the calibrated instrument is used as a reference.

For calibration management, expanded uncertainty is the primary uncertainty metric tracked and compared. It determines whether a laboratory has sufficient capability (TUR) for specific calibrations, appears on calibration certificates as required by ISO 17025, and feeds into customer uncertainty budgets. Organizations should ensure that expanded uncertainty values on calibration certificates are understood and properly used — including propagating reference standard uncertainty into the uncertainty budget when the calibrated instrument is used to calibrate other instruments downstream.