  Following the set up in arXiv:1408.3393, we study 4d N=1 superconformal field
theories in conic spaces. We show that the universal part of supersymmetric
R\'enyi entropy S_q across a spherical entangling surface in the limit q goes
to 0 is proportional to a linear combination of central charges, 3c-2a. This is
equivalent to a similar statement about the free energy of SCFTs on conic space
or hyperbolic space S^1_q*H^3 in the corresponding limit. We first derive the
asymptotic formula by the free field computation in the presence of a U(1)
R-symmetry background and then provide an independent derivation by studying
N=1 theories on a primary Hopf surface S^1_\beta*S^3_b with a particular
scaling \beta~1/\sqrt{q} and b=\sqrt{q}, which thus confirms the validity of
the formula for general interacting N=1 SCFTs. Finally we revisit the
supersymmetric R\'enyi entropy of general N=2 SCFTs and find a simple formula
for it in terms of central charges a and c.
