  We study a supersymmetric, rotating, electrically charged black hole in
AdS$_{4}$ which is a solution of four-dimensional minimal gauged supergravity.
Using holography we show that the free energy on $S^3$ and the superconformal
index of the dual three-dimensional $\mathcal N=2$ SCFT, in the planar limit,
are related in a simple universal way. This result applies to large classes of
SCFTs constructed from branes in string and M-theory which we discuss in some
detail. For theories of class $\mathcal R$, which arise from $N$ M5-branes
wrapped on hyperbolic three-manifolds, we show that the superconformal index
agrees with the black hole entropy in the large $N$ limit.
