Combined & Expanded Uncertainty (RSS)
Combine up to five standard-uncertainty contributions by RSS and multiply by the coverage factor for expanded uncertainty.
Worked example
Input: Standard uncertainty u₁ 1 dB, Standard uncertainty u₂ 0.5 dB, Standard uncertainty u₃ 0.3 dB, Standard uncertainty u₄ 0.8 dB, Standard uncertainty u₅ 0.2 dB, Coverage factor k 2
Result: Combined standard uncertainty u_c 1.42127 dB, Expanded uncertainty U = k·u_c 2.84253 dB
Result: Combined standard uncertainty u_c 1.42127 dB, Expanded uncertainty U = k·u_c 2.84253 dB
Formula
u_c = √(u₁² + u₂² + … + u₅²)
U = k · u_c (k = 2 → about 95 %)
How it works
Independent uncertainty components combine as the root of the sum of squares (RSS). Multiplying the combined standard uncertainty u_c by a coverage factor k (typically 2, about 95 %) gives the expanded uncertainty U. Convert receiver error, cable loss, antenna factor, mismatch, repeatability and so on to standard uncertainties first.
Practical tipConvert each term to a standard uncertainty before entering it. A ± value on a certificate is usually a half-width, so divide it by the divisor for the right distribution (√3 for rectangular). The "Uncertainty distribution divisor" calculator does exactly that.
Related calculators
Related standards
Related guides
Results and summaries are for reference. For certification and test reports use the latest official standard text and calibrated instrument data. Last updated: 2026-10-10