  We provide a consistent first principles prescription to compute
gravitational R\'enyi entropy using Hayward corner terms. For Euclidean
solutions to Einstein gravity, we compute R\'enyi entropy of Hartle--Hawking
and fixed--area states by cutting open a manifold containing a conical
singularity into a wedge with a corner. The entropy functional for fixed--area
states is equal to the corner term itself, having a flat-entanglement spectrum,
while extremization of the functional follows from the variation of the corner
term under diffeomorphisms. Notably, our method does not require regularization
of the conical singularity, and naturally extends to higher-curvature theories
of gravity.
