Results of a systematic analysis of actual vs. estimated uncertainty in scientific models are presented. Data sets include: i) time trends in the sequential measurements of the same physical quantity; ii) national population projections; iii) projections for the United States' energy sector. Probabilities of large deviations from the true values are parametrized by an exponential distribution with the slope determined by the data. An alternative parametrization by Levy stable distributions, based on the fractal model for the distribution of errors, is described. In practice, one can hedge against unsuspected uncertainties by inflating the reported uncertainty range by a default safety factor determined from the relevant historical data sets. This empirical approach can be used in the uncertainty analysis of the low probability/high consequence events (such as risk to public health from exposure to electromagnetic fields or risk of extreme sea-level rise resulting from global warming).