We present a new library of fully-radiative shock models calculated with the MAPPINGS iii shock and photoionization code . The library consists of grids of models with shock velocities in the range v _ { s } =100-1000 km s ^ { -1 } and magnetic parameters B/ \sqrt { n } of 10 ^ { -4 } -10 \mu G cm ^ { 3 / 2 } for five different atomic abundance sets , and for a pre-shock density of 1.0 cm ^ { -3 } . Additionally , Solar abundance model grids have been calculated for densities of 0.01 , 0.1 , 10 , 100 , and 1000 cm ^ { -3 } with the same range in v _ { s } and B/ \sqrt { n } . Each model includes components of both the radiative shock and its photoionized precursor , ionized by the EUV and soft X-ray radiation generated in the radiative gas . We present the details of the ionization structure , the column densities , and the luminosities of the shock and its precursor . Emission line ratio predictions are separately given for the shock and its precursor as well as for the composite shock+precursor structure to facilitate comparison with observations in cases where the shock and its precursor are not resolved . Emission line ratio grids for shock and shock+precursor are presented on standard line ratio diagnostic diagrams , and we compare these grids to observations of radio galaxies and a sample of AGN and star forming galaxies from the Sloan Digital Sky Survey . This library is available online , along with a suite of tools to enable the analysis of the shocks and the easy creation of emission line ratio diagnostic diagrams . These models represent a significant increase in parameter space coverage over previously available models , and therefore provide a unique tool in the diagnosis of emission by shocks .