2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137136An analogue of the Berry-Esseen inequality is proved for the speed of convergence of free additive convolutions of bounded probability measures. The obtained rate of convergence is of the order n^{-1/2}, the same as in the classical case. An example with binomial measures shows that this estimate cannot be improved without imposing further restrictions on convolved measures.15 pages, accepted to the Journal of Theoretical Probability, minor typos are corrected in versions 2 and 3ProbabilityOperator Algebras46L54; 60F05text