This article covers the development of algorithms for predicting the frequencies of explosions based on a variety of design, operating and environmental conditions. Algorithms were developed fir estimating unit-based explosion frequencies, such as those reported in API, but in more detail and covering a much broader range of chemical process types. This article also shows the developed methods for predicting scenario-based explosion frequencies, using frequencies of initiating events and conditional probabilities of immediate ignition and delayed ignition resulting in explosion. The algorithms were based on a combination of published data and expert opinion. (C) 2009 American Institute of Chemical Engineers Process Saf Prog 29: 155-161, 2010