GIFSQ Tools · Module 15 — Metrology, Validation & Laboratory Accreditation · Tool 281 of 500
Combine the standard uncertainty components of a measurement into a combined standard uncertainty and an expanded uncertainty at your chosen coverage factor — the core calculation of Eurachem/CITAC CG4.
Try sample values — fills the form with the worked example below.
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Combined uncertainty (uᶜ)
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Expanded uncertainty (U)
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Relative expanded uncertainty (%)
Equation: uᶜ = √(u₁² + u₂² + … + uₙ²). Expanded uncertainty U = k × uᶜ. Relative U (%) = U ÷ result × 100.
Method: Root-sum-of-squares combination with a coverage factor, per Eurachem/CITAC Guide CG4 (Quantifying Uncertainty in Analytical Measurement) and the Guide to the Expression of Uncertainty in Measurement (GUM, JCGM 100). k = 2 gives approximately 95% coverage for a normal distribution.
Assumptions: the components are independent (uncorrelated) and already expressed as standard uncertainties (one standard deviation); the result is approximately normally distributed.
Limitations: correlated components need covariance terms, which this tool does not include; k = 2 is only approximately 95% coverage when the effective degrees of freedom are small — use the Welch–Satterthwaite equation for a rigorous coverage factor.
Rounding: combined and expanded uncertainty to 2 decimal places; relative uncertainty to 2 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Method: Root-sum-of-squares combination with a coverage factor, per Eurachem/CITAC Guide CG4 (Quantifying Uncertainty in Analytical Measurement) and the Guide to the Expression of Uncertainty in Measurement (GUM, JCGM 100). k = 2 gives approximately 95% coverage for a normal distribution.
Assumptions: the components are independent (uncorrelated) and already expressed as standard uncertainties (one standard deviation); the result is approximately normally distributed.
Limitations: correlated components need covariance terms, which this tool does not include; k = 2 is only approximately 95% coverage when the effective degrees of freedom are small — use the Welch–Satterthwaite equation for a rigorous coverage factor.
Rounding: combined and expanded uncertainty to 2 decimal places; relative uncertainty to 2 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Worked example: Components 0.5, 0.3 and 0.4 mg/kg with k = 2 on a result of 100 mg/kg: uᶜ = √(0.25 + 0.09 + 0.16) = 0.71 mg/kg, U = 2 × 0.71 = 1.41 mg/kg, relative U = 1.41%.
Enter values above to see results.
Typical k: 2 for about 95% coverage, 3 for about 99.7%. Report as result ± U with the k value stated. Tool 281 of 500 — GIFSQ
