Coverage Factor ($k$) is the multiplier applied to the combined standard uncertainty to obtain the expanded uncertainty — $U = k cdot u_c$, chosen to provide a specified level of confidence (typically 95% or 99.7%) that the true value lies within the expanded uncertainty interval.

Coverage Factor Values

• k = 1: ~68% confidence (1 standard deviation) — rarely used for reporting.
• k = 2: ~95% confidence — the default for most measurement reports and calibration certificates.
• k = 3: ~99.7% confidence — used for safety-critical applications and process control (3σ limits).
• Student's t: When effective degrees of freedom are small (<30), use $k = t_{p,

u_{eff}}$ from tables instead of $k = 2$.

Why It Matters

• Risk Balance: Higher $k$ reduces the risk of the true value being outside the stated uncertainty — but widens the interval.
• Welch-Satterthwaite: The effective degrees of freedom ($

u_{eff}$) determine the appropriate $k$ — calculated from individual component DOF.

• Context: Always state the coverage factor and confidence level — "U = 0.5nm (k=2, 95% confidence)."

Coverage Factor is the confidence multiplier — scaling combined uncertainty to provide a desired level of confidence in the measurement result.