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Randozi
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Combined Standard Uncertainty Calculator

Enter the standard uncertainties of your measurements and their sensitivity coefficients, and get the combined standard uncertainty. Choose independent components or a pair with a correlation.

Combined standard uncertainty u_c

0.223607

Expanded uncertainty U = k × u_c = 0.447214

  • Component 1

  • Component 2

Standard uncertainties are standard deviations, not plus-minus limits. Use the independent formula only if you have no reason to expect a shared error source.

How it works

  1. Pick independent components, or a correlated pair.
  2. Enter each standard uncertainty (a standard deviation) and its sensitivity coefficient; leave 1 if the quantity is added directly.
  3. For a pair, enter the correlation between −1 and 1.
  4. Read the combined uncertainty, optionally multiply by a coverage factor you choose, and copy it.

What people use it for

  • A measurement with several error sources

    Combine the repeatability of a gauge, its calibration and the resolution of a display into one figure.

  • Seeing what correlation changes

    Compare the same two components at a correlation of −1, 0 and +1.

  • Checking a lab spreadsheet

    Verify a root-sum-square by hand against a second tool.

Questions

What is the formula?
For independent components u_c = √(Σ (a × u)²). For two components with correlation ρ: u_c = √((a₁u₁)² + (a₂u₂)² + 2 × a₁ × a₂ × ρ × u₁ × u₂), kept at 0 if rounding makes it slightly negative.
Can I combine plus-minus tolerances this way?
No. A tolerance printed on a drawing is a limit, not a standard deviation, and combining limits this way gives no probability. Use the worst-case tolerance stack-up page for limits.
What does the coverage factor do?
It multiplies the combined uncertainty to give an expanded uncertainty, U = k × u_c. A factor of 2 is a common convention for roughly 95 % coverage only when the result is close to normally distributed. You choose k; the page does not claim a probability.
How do I know whether two errors are correlated?
If one error source affects both quantities (the same gauge, the same temperature), they are probably correlated. If you do not know, the independent formula is an assumption you should state.