Impactors are designed according to numerical computations, which have been shown to give accurate predictions for the 50% cutpoint. However, such computer calculations obscure the basic physics of the impactor. Textbook derivations commonly assume circular streamlines and do not yield accurate results for the cutpoint. In this paper, a simple but accurate derivation is given for the cutpoint of an impactor with a rectangular nozzle, based on only very general assumptions as to the flow. For an impactor with a circular nozzle, the derivation requires an additional input datum and is less accurate. The derivation makes clear the essential physics of the impactor.