First-principles calculations are performed to investigate structural and magnetic behaviors of rare-earth orthochromates as a function of 'chemical' pressure (that is, the rare-earth ionic radius), epitaxial misfit strain and hydrostatic pressure. From a structural point of view, (i) 'chemical' pressure significantly modifies antipolar displacements, Cr-O-Cr bond angles and the resulting oxygen octahedral tiltings; (ii) hydrostatic pressure mostly changes Cr-O bond lengths; and (iii) misfit strain affects all these quantities. The correlations between magnetic properties (Néel temperature and weak ferromagnetic moments) and unit cell volume are similar when varying the misfit strain or hydrostatic pressure, but differ from those associated with the 'chemical' pressure. Origins of such effects are also discussed.