  We give an explicit formula for the quaternionic K\"ahler metrics obtained by
the HK/QK correspondence. As an application, we give a new proof of the fact
that the Ferrara-Sabharwal metric as well as its one-loop deformation is
quaternionic K\"ahler. A similar explicit formula is given for the analogous
(K/K) correspondence between K\"ahler manifolds endowed with a Hamiltonian
Killing vector field. As an example, we apply this formula in the case of an
arbitrary conical K\"ahler manifold.
