Independent Measurement Uncertainty Calculator
Propagate independent standard uncertainties through a sum, difference, product or quotient using first-order sensitivities.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Evaluate the function and its partial derivatives, multiply each derivative by its input standard uncertainty and combine independent contributions in quadrature.
u(f)=√[(∂f/∂x ux)²+(∂f/∂y uy)²]; expanded uncertainty=k u(f)
Worked example
x=10±0.2 and y=5±0.1 give product 50 with standard uncertainty √2≈1.4142. With k=2, expanded uncertainty is approximately 2.8284.
Assumptions and input details
Input ± values are standard uncertainties, not worst-case bounds or confidence limits. Independent inputs, zero covariance and first-order linearization are assumed. Sums/differences need compatible units; products/quotients use the resulting compound unit. The quotient denominator must be nonzero, and linearization can be unreliable when denominator uncertainty is large relative to its magnitude. The entered expansion factor alone does not establish coverage probability.
References: NIST: law of propagation of uncertainty
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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