I define a measure of rationality based on standard concepts from information theory. I obtain a characterization result, as well as an alternative characterization based on a different axioms. Given a dataset, I provide bounds on rationality depending on observed behavior. When the data is generated by utility maximization with error, as in a logit model, the measure of rationality can be micro-founded. This creates a natural bridge between definitions of rationality from the fields of decision theory and behavioral welfare economics, providing a unifying framework for analyzing (ir-)rational behavior.