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On Higher Order Corrections for Propagating Uncertainties



Chih-Ming Wang, Hariharan K. Iyer


The ISO Guide to the Expression of Uncertainty in Measurement (GUM) recommends the use of a first-order Taylor series expansion for propagating errors and uncertainties. The GUM also suggests the use of a second-order Taylor series approximation for calculating uncertainties when the first-order approximation alone is not adequate. In this paper we derive the formulas for evaluating measurement uncertainty based on a second-order Taylor series approximation. We provide a computer program that uses symbolic derivatives to calculate the second-order approximations of the uncertainty in measurement results.


GUM, propagation of error, software, Taylor series expansion


Wang, C. and Iyer, H. (2005), On Higher Order Corrections for Propagating Uncertainties, Metrologia (Accessed May 20, 2024)


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Created December 31, 2004, Updated October 12, 2021