  We calculate the constraints on the primordial curvature perturbation at the
end of inflation from the present day abundance of Primordial Black Holes
(PBHs), as a function of the reheat temperature T_{\rm RH}. We first extend
recent work on the formation of PBHs on scales which remain within the horizon
during inflation and calculate the resulting constraints on the curvature
perturbation. We then evaluate the constraint from PBHs that form, more
conventionally, from super-horizon perturbations. The constraints apply for
T_{\rm RH} < 10^{8} GeV and the inclusion of sub-horizon PBHs leads to a limit
which is roughly three times tighter than the bound from super-horizon PBHs.

Astrophysics;General Relativity and Quantum Cosmology