  We develop a formalism to compute the gravitational multipole moments and
ratios of moments of non-extremal and of supersymmetric black holes in four
dimensions, as well as of horizonless microstate geometries of the latter. For
supersymmetric and for Kerr black holes many of these multipole moments vanish,
and their dimensionless ratios are ill-defined. We present two methods to
compute these dimensionless ratios, which for certain supersymmetric black
holes agree spectacularly. We also compute these dimensionless ratios for the
Kerr solution. Our methods allow us to calculate an infinite number of hitherto
unknown parameters of Kerr black holes, giving us a new window into their
physics.
