Propagate independent standard uncertainties through addition, subtraction, product, ratio or a fixed power, with sensitivity coefficients.
Your input
Outputs are cleared when the input changes.
Result
Enter your data or use the example, then run the tool.
Worked example
Adding 10 with u=1 and 20 with u=2 gives value 30 and combined standard uncertainty √5.
Multiplying a value by the exact constant 2 doubles its standard uncertainty; set the constant’s uncertainty to zero.
Method
For f, use uc² = Σ(∂f/∂xi)²ui² for independent inputs. Show the derivatives and signed standard contributions.
A hypot-based sum combines contributions. Power p is a known constant; relative uncertainty is undefined when the function value is zero.
Limits
No correlations, covariance, expanded uncertainty or calibration certification. Large relative uncertainties in nonlinear functions can invalidate first-order approximation.
Uncertainties must be non-negative; denominator zero and non-real or undefined power derivatives are rejected. Keep physical units consistent.
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