Abstract. For a dynamical system (X, T ) and function f : X → R d we consider the corresponding generalised rotation set. This is the convex subset of R d consisting of all integrals of f with respect to T -invariant probability measures. We study the entropy H( ) of rotation vectors , and relate this to the directional entropy H( ) of Geller & Misiurewicz. For (X, T ) a mixing subshift of finite type, and f of summable variation, we prove that if the rotation set is strictly convex then the functions H and H are in fact one and the same. For those rotation sets which are not strictly convex we prove that H( ) and H( ) can differ only at non-exposed boundary points .