Scan statistics are commonly used in biology, medicine, engineering and other fields where interest is in the probability of observing clusters of events in a window at an unknown location. Due to the dependent nature of the number of events in a large number of overlapping window locations, even approximate solutions for the simplest scan statistics may require elaborate calculations. We propose a new martingale method which allows one to approximate the distribution for a wide variety of scan statistics, including some for which analytical results are computationally infeasible.