We calculate the probability ͑''quenching weight''͒ that a hard parton radiates an additional energy fraction ⌬E due to scattering in spatially extended QCD matter. This study is based on an exact treatment of a finite in-medium path length; it includes the case of a dynamically expanding medium, and it extends to the angular dependence of the medium-induced gluon radiation pattern. All calculations are done in the multiple soft scattering approximation ͓Baier-Dokshitzer-Mueller-Peigné-Schiff-Zakharov ͑BDMPSZ͒ formalism͔ and in the single hard scattering approximation ͓Nϭ1 opacity approximation͔. By comparison, we establish a simple relation between the transport coefficient, Debye screening mass and opacity, for which both approximations lead to comparable results. Together with this paper, a CPU-inexpensive numerical subroutine for calculating quenching weights is provided electronically. To illustrate its applications, we discuss the suppression of hadronic transverse momentum spectra in nucleus-nucleus collisions. Remarkably, the kinematic constraint resulting from finite in-medium path lengths reduces significantly the p Ќ dependence of the nuclear modification factor, thus leading to consistency with the data measured at the BNL Relativistic Heavy Ion Collider.