This paper is a study of Bentham's felicific calculus. Challenging a view that contrasts 'cardinal' to 'ordinal' calculus, we show that these two forms of calculus constitute instead different phases of a single approach. Bentham sometimes has to rely upon proxy variables because of operational constraints, and consequently upon factors other than utility. As a utilitarian, Bentham is de facto welfarist from an ethical point of view. Surprisingly however, this study shows that Bentham resorts to non-welfare information in the actual application of his calculus. His approach reconciles non-welfarism from the technical standpoint with welfarism as a fundamental moral principle.