We study the formation of primordial black holes (PBHs) from large primordial perturbations that re-enter the horizon during an epoch with equation of state w ≥ 1/3. We consider a log-normal curvature power spectrum of finite width ∆ and determine the collapse amplitude by numerical-relativity simulations of a self-gravitating perfect fluid. Threshold scans are performed for five values of w and five spectral widths, and the resulting numerical thresholds are used in the PBH abundance and scalar-induced gravitational-wave (SIGW) calculations. For comparison, we also evaluate two calibrations of the semi-analytical wq-prescription and find that, while they may reproduce the numerical threshold within a 2.8–8% error, this precision is often insufficient for PBH abundance computations. We show how collapse thresholds increase with both ∆ and w, changing the curvature amplitude required for PBHs to constitute all of the dark matter and, consequently, the normalization of the associated SIGW signal.