For uniformly expanding maps on the interval, analogous versions of the Berry-Ess\'een theorem are known but only with an unexplicit upper bound in $O(1/\sqrt{n})$ without any constants being specified. In this paper, we use the recent complex cone technique to prove an explicit Berry-Ess\'een estimate with a reasonable constant for these maps. Our method is not limited to maps on the interval however and should apply to many situations.