Calculate GUM-compliant expanded uncertainty from your Type A and Type B components. Free, instant results — no signup required.
This calculator implements the uncertainty evaluation process described in the GUM (Guide to the Expression of Uncertainty in Measurement, ISO/IEC Guide 98-3). It combines Type A and Type B uncertainty components using the root-sum-square (RSS) method, applies the appropriate coverage factor, and optionally computes the Welch-Satterthwaite effective degrees of freedom.
Each component is converted to a standard uncertainty using the divisor for its probability distribution: √3 for rectangular, √6 for triangular, and 2 for normal (k=2). The sensitivity coefficient scales each component's contribution to the combined uncertainty.
Measurement uncertainty quantifies the doubt about a measurement result. It expresses the range of values within which the true value is expected to lie, at a stated confidence level. ISO/IEC 17025 requires calibration laboratories to evaluate and report measurement uncertainty.
The GUM (Guide to the Expression of Uncertainty in Measurement, ISO/IEC Guide 98-3) is the internationally accepted framework for evaluating measurement uncertainty. It classifies uncertainty sources as Type A (statistical analysis of repeated measurements) or Type B (other methods such as manufacturer specifications, calibration certificates, or engineering judgment).
The coverage factor (k) multiplies the combined standard uncertainty to produce the expanded uncertainty. A coverage factor of k=2 corresponds to approximately 95% confidence for a normal distribution. The appropriate k value may differ based on the effective degrees of freedom calculated via the Welch-Satterthwaite formula.
Use rectangular (uniform) when you only know the bounds with no information about the distribution shape — this is the most common. Use triangular when values near the center are more likely. Use normal when the source provides an expanded uncertainty at a known confidence level.