Measurement Uncertainty Calculator
GUM first-order uncorrelated uncertainty budget with entered sensitivities and coverage factor. Coverage probability is not inferred.
In short
GUM first-order uncorrelated uncertainty budget with entered sensitivities and coverage factor. Coverage probability is not inferred.
Formula: For uncorrelated inputs: u_c = √Σ(cᵢuᵢ)²; expanded uncertainty U = k u_c.
What this calculator does
GUM first-order uncorrelated uncertainty budget with entered sensitivities and coverage factor. Coverage probability is not inferred. Formula, worked example, sources, FAQs and limitations included.
Use it to turn Input standard uncertainties uᵢ (not raw observations), Sensitivity coefficients cᵢ in matching order, Declared coverage factor k (not a confidence percentage) into a checked result you can compare, copy, or rerun with different assumptions.
The page shows the formula, a numeric worked example, and the assumptions that affect this statistics calculation.
Inputs and what they mean
- Input standard uncertainties uᵢ (not raw observations)
- — text value.
- Sensitivity coefficients cᵢ in matching order
- — text value.
- Declared coverage factor k (not a confidence percentage)
- — number value.
How to use it
- Enter each value in the unit shown next to the box (use the unit converter first if your numbers are in other units).
- Check the breakdown to see every intermediate step.
- Read the limitations before relying on the result.
Formula
Methodology type: scientific equation.
Methodology: JCGM 100:2008 GUM §§5–6, first-order propagation restricted to uncorrelated input quantities.
Observations on this page are input standard uncertainties uᵢ. Sensitivity coefficients must convert each contribution into the output's unit.
Correlated inputs require covariance terms, omitted only under the declared uncorrelated-input assumption. Significant nonlinearity needs a different method.
k = 2 does not universally guarantee 95% coverage; the coverage basis is external to this calculator.
For uncorrelated inputs: u_c = √Σ(cᵢuᵢ)²; expanded uncertainty U = k u_c.
Worked example
Combined standard uncertainty
- u_c = √(3² + 4²) = 5 output units.
- U = 2 × 5 = 10 output units; no coverage probability inferred.
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
Limitations and assumptions
- Uncorrelated first-order uncertainty budget only.
- No covariance, nonlinear Monte Carlo or effective degrees-of-freedom calculation.
- For education and operational analysis only. No diagnosis, treatment recommendations, prescribing, dosing instructions, or reimbursement entitlement. Scientific calculations require appropriate laboratory verification; operational estimates do not replace local clinical, safety or financial policies.
- The result depends on the values you enter for this measurement uncertainty calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.
Reference: JCGM / BIPM
Last reviewed:
Common questions
Are these raw observations?
No. Enter already evaluated standard uncertainties and matching sensitivity coefficients.
What if inputs are correlated?
This version does not support covariance. Do not use it when correlations contribute materially.
Does k = 2 mean exactly 95%?
No. Coverage depends on the output distribution, effective degrees of freedom and justified coverage method.
How do I use the Measurement Uncertainty Calculator?
Enter the required values for Input standard uncertainties uᵢ (not raw observations), Sensitivity coefficients cᵢ in matching order, Declared coverage factor k (not a confidence percentage). The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.
What formula does the Measurement Uncertainty Calculator use?
For uncorrelated inputs: u_c = √Σ(cᵢuᵢ)²; expanded uncertainty U = k u_c. The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone.
Can the Measurement Uncertainty Calculator be used for exact decisions?
Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.
Sources
Method based on JCGM / BIPM.
Cite this page
Free Calculator. (2026, October 23). Measurement Uncertainty Calculator. https://freecalculator.tech/tools/measurement-uncertainty-calculator
"Measurement Uncertainty Calculator." Free Calculator, 23 Oct. 2026, https://freecalculator.tech/tools/measurement-uncertainty-calculator.
Measurement Uncertainty Calculator — Free Calculator, https://freecalculator.tech/tools/measurement-uncertainty-calculator
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