Let {φt}t >= 0 be a semigroup of holomorphic self-maps of the unit disk. We assume that the Denjoy–Wolff point of the semigroup is the point 1; so 1 is the unique attractive boundary fixed point of the semigroup. We further assume that for all t > 0, φt(1) < 1 (angular derivative), namely the semigroup is hyperbolic. We prove then that the rate of convergence of the semigroup to t…