Estimating the number of substitution events per site that have occurred during the evolution of a pair of amino acid sequences is a common task in phylogenetics and comparative genomics that often requires quite slow maximum-likelihood procedures when taking into account explicit evolutionary models. Data presented in this article are large sets of numbers of substitution events and associated numbers of observed differences between pairs of aligned amino acid sequences that have been generated through a simulation procedure of sequence evolution under a broad range of evolutionary models. These data are available at https://zenodo.org/record/2653704 (doi:10.5281/zenodo.2653704). They are accompanied in this paper by figures showing the strong relationship between the corresponding evolutionary and uncorrected distances, as well as estimated numerical constants that determine non-linear functions that fit the simulated data. These numerical constants can be useful to quickly estimate pairwise evolutionary distances directly from uncorrected distances between aligned amino acid sequences.