Combine accuracy, resolution, and an additional independent uncertainty component by root-sum-square.
Why it matters: A measured difference should not be over-interpreted when it is comparable to the combined measurement uncertainty.
ΣCALCULATE · VERIFY · INTERPRET
Calculated result
Engineering evaluation
Within entered screening criteria
Combined relative standard uncertainty (Ur)1.118 %
Entered percent-of-reading standard uncertainty component (Ua)
1 selected units
Resolution component (Ures)
0.029 selected units
Combined standard uncertainty (U)
1.118 selected units
Engineering interpretation
The combined standard uncertainty is 1.118 selected units, or 1.118% of the reading, compared with the entered 2% relative-uncertainty limit. This screening combination assumes independent standard components and does not automatically provide expanded uncertainty or a coverage interval.
Important limitations
The percent-of-reading input is treated as a standard uncertainty component. Convert a published accuracy limit to an appropriate standard uncertainty before formal analysis, and verify the entered project criterion.
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Understand the calculation—not just the answer
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Governing relationships
Ua = |X|A/100
Ures = R/√12
U = √(Ua²+Ures²+Uo²)
Ur = U/|X|×100
within entered criterion when Ur ≤ L
Current substitution
Ua = |100|×1/100 = 1; Ures = 0.1/√12 = 0.02887; U = 1.118; Ur = 1.118%.
Calculation sequence
Step-by-step method
Convert the entered percent-of-reading standard uncertainty to an absolute component.
Represent digital resolution as a rectangular standard uncertainty.
Combine independent standard uncertainty components by root-sum-square and divide by reading magnitude.
Equation legend
Inputs and calculated quantities
X
Measured reading — selected units
A
Percent-of-reading standard uncertainty component — % of reading
R
Display resolution — selected units
Uo
Other independent standard uncertainty — selected units
L
Entered maximum relative uncertainty — %
Ur
Combined relative standard uncertainty — %
Ua
Entered percent-of-reading standard uncertainty component — selected units
Ures
Resolution component — selected units
U
Combined standard uncertainty — selected units
Applications
How this calculation is used
Building design
Screen whether planned instrumentation can resolve the required acceptance band.
Construction
Support instrument selection and test planning.
Commissioning
Estimate combined standard uncertainty and relative uncertainty for a field reading.
Quality controls
Assumptions and limitations
Assumptions
Entered values represent the same stable operating condition.
Measurements and reference values use consistent units and boundaries.
Limitations
This is a screening and field-verification tool, not an automatic acceptance decision.
Confirm the approved reference values and test boundary.
Stabilize the system and record calibrated field measurements.
Review calculation assumptions, uncertainty, and supporting evidence before disposition.
Common engineering mistakes
Comparing readings taken at different loads, modes, or reference conditions.
Treating a calculated status as proof of code, contract, or manufacturer compliance.
Technical basis
References and source standards
NIST Technical Note 1297Guidance for evaluating and expressing measurement uncertainty, including root-sum-square combination of independent standard uncertainty components.
These engineering tools are provided for educational, preliminary evaluation, field verification, and commissioning support. Results depend on the accuracy of user-entered information and the assumptions stated for each calculation. Every colored status and comparison is a screening indicator only; project criteria, contract requirements, applicable codes, manufacturer instructions, measurement uncertainty, and authorized engineering judgment govern. The tools do not replace project-specific engineering analysis or the judgment of a licensed professional engineer.
