The dependence of structural and magnetic properties of rare-earth orthoferrites (in their Pbnm ground state) on the rare-earth ionic radius is systematically investigated from first principles. The effects of this 'chemical pressure' on lattice constants, Fe-O bond lengths, Fe-O-Fe bond angles and Fe-O bond length splittings are all well reproduced by these ab initio calculations. The simulations also offer novel predictions (on tiltings of FeO6 octahedra, cation antipolar displacements and weak magnetization) to be experimentally checked. In particular, the weak ferromagnetic moment of rare-earth orthoferrites is predicted to be a linear function of the rare-earth ionic radius. Finally, the effects of applying hydrostatic pressure on structural and magnetic behavior of SmFeO3 is also studied. It is found that, unlike previously assumed, hydrostatic pressure typically generates changes in physical properties that are quantitatively and even qualitatively different from those associated with the chemical pressure.