Propagation of Uncertainty Rules for Estimating Uncertainty

Propagation of Uncertainty

Propagation of uncertainty is a method that transmits the uncertainties of independent variables through an equation to estimate the uncertainty of the final calculation. When physical quantities cannot be measured with a single direct measurement, we typically perform indirect measurements of two or more quantities to calculate the desired measurement result. By applying this methodology, we must estimate the uncertainty of our independent measurement results and use propagation rules to estimate the uncertainty of the final calculation.


Rules for Propagating Uncertainty

To properly propagate uncertainty, there are rules that must be followed. These rules allow us to propagate uncertainty for many different types of physical equations. To help, I have compiled a list of many of the common mathematical functions encountered when calculating measurement results. Refer to the chart below for the rules of propagating uncertainty.




For an example of applying these rules, please see my article How to Propagate Uncertainty. If you have any questions or comments, please feel free to contact me at [email protected].

About the Author

Richard Hogan

Richard Hogan is the CEO of ISO Budgets, L.L.C., a U.S.-based consulting and data analysis firm. Services include measurement consulting, data analysis, uncertainty budgets, and control charts. Richard is a systems engineer who has laboratory management and quality control experience in the Metrology industry. He specializes in uncertainty analysis, industrial statistics, and process optimization. Richard holds a Masters degree in Engineering from Old Dominion University in Norfolk, VA. Connect with Richard on LinkedIn.


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