THE FEUTEX TOOLKIT

Correlated Measurement Uncertainty

Propagate correlated standard uncertainties through a sum, difference and product.

Statistics workspace● Runs in your browser

01 Your input

First measured valuevalueSecond measured valuevalueFirst standard uncertaintyvalueSecond standard uncertaintyvalueError correlationcorrelation

02 Your result

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Result data

Formula

Sum Uncertainty = sqrt(max(0,ux**2+uy**2+2*rho*ux*uy)); Difference Uncertainty = sqrt(max(0,ux**2+uy**2-2*rho*ux*uy)); Product Uncertainty = sqrt(max(0,y**2*ux**2+x**2*uy**2+2*x*y*rho*ux*uy))

Sources and model references

https://physics.nist.gov/cuu/Uncertainty/combination.html

Worked example

Inputs

First measured value: 10 value
Second measured value: 5 value
First standard uncertainty: 0.2 value
Second standard uncertainty: 0.1 value
Error correlation: 0.5 correlation

Expected results

Sum Uncertainty: 0.2645751311 number
Difference Uncertainty: 0.1732050808 number
Product Uncertainty: 1.732050808 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

Enter the labeled inputs using consistent units.
Check the stated assumptions and calculate.
Review each output and compare another input scenario.

Try this example

{
  "x": 10,
  "y": 5,
  "ux": 0.2,
  "uy": 0.1,
  "rho": 0.5
}

Accuracy and scope

First-order uncertainty propagation; product approximation assumes small uncertainties and known correlation. Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.