A finite-differences technique for propagating uncertainty in calculations

The propagation of errors in calculations is conventionally treated analytically. This Journal recently published a new treatment based on a numerical simulation method using pseudorandom numbers. This article presents a deterministic method that requires less extra computation than the simulation method, uses the directly estimated true value and uncertainty for each measured quantity, and naturally generates estimates of the contributions to the uncertainty from each source. By avoiding the relatively subtle concept of the covariances of the measured quantities, the method presented here is more readily appreciated by intermediate level students (physics majors or nonscientists), although it cannot be used to determine whether the random errors of measurement are correlated.