Results from dispersion models which are routinely used for regulatory purposes do not reflect the uncertainties which are inherent in the input data. To remedy this, a formula for propagating measurement uncertainties of emission rate, wind speed, wind direction, horizontal dispersion parameter, vertical dispersion parameter, effective emission height, and mixing depth is derived for EPA's Industrial Source Complex Short Term (ISCST) Gaussian dispersion model for the simple case of a single stack-type source and nonbuoyant plume. Values for the uncertainties of the input variables are chosen and used to calculate ambient concentration uncertainties. These calculated uncertainties are compared with the standard deviation of ambient concentrations calculated from 2500 input data sets for each of four stability classes and three downwind distances, which were randomly altered to simulate the effects of measurement uncertainty. The calculated uncertainties do not differ significantly from the standard deviations of the randomized calculations for input data uncertainties as high as 30 percent and Stability Classes A-C. The calculated uncertainties overestimate the actual uncertainty of model calculations for input data uncertainties greater than 20 percent for Stability Class D.