We define maximum entropy goal-directedness (MEG), a formal measure of goal-directedness in causal models and Markov decision processes, and give algorithmsfor computing it. Measuring goal-directedness is important, as it is a criticalelement of many concerns about harm from AI. It is also of philosophical interest,as goal-directedness is a key aspect of agency. MEG is based on an adaptation ofthe maximum causal entropy framework used in inverse reinforcement learning. Itcan measure goal-directedness with respect to a known utility function, a hypothesisclass of utility functions, or a set of random variables. We prove that MEG satisfiesseveral desiderata and demonstrate our algorithms with small-scale experiments.