Cycles in revealed preference data are often regarded as fundamental units of choice-theoretic inconsistency. Contrary to this, we show that in nearly any environment, cyclic choices over some menus necessarily force further cyclic choices elsewhere. In many cases, the entirety of a subject’s inconsistency can be explained by only a handful of cycles. We characterize such dependencies, and show that every set of `independent’ cycles capable of explaining all others is necessarily of the same size. This quantity provides a simple, transparent measure of irrationality that accounts for the dependencies introduced by the structure of the choice environment or experiment.