The super-twisting algorithm is a well-known technique in the field of sliding mode control or observation. In this contribution, an exact analytic expression for this algorithm's finite reaching time in the unperturbed case is derived. Based on this derivation, a novel estimation for the upper bound of the algorithm's reaching time the presence of perturbations is presented. The considered perturbations may be composed of additive components that are either Lipschitz continuous in time or Holder continuous in the sliding variable. Both analytically and in the course of numerical examples the new strategy is shown to yield significant improvements compared to existing reaching time estimates.