Transverse Peltier coolers have been experimentally and theoretically studied since 1960s due to their capability of achieving cooling in a single-leg geometry. Recently proposed pxn-type transverse thermoelectrics reveal the possibility of intrinsic or undoped transverse coolers that can, in principle, function at cryogenic temperatures, which has drawn more attention to the performance of such transverse coolers. However, unlike longitudinal thermoelectrics, the equations for transverse thermoelectrics cannot be solved analytically. In this study, we therefore calculate the thermoelectric transport in transverse coolers numerically, and introduce a normalized notation, which reduces the independent parameters in the governing equations to a normalized electric field E* and a hot-side transverse figure of merit zTh, only. A numerical study of the maximum cooling temperature difference and cooling power reveals the superior performance of transverse thermoelectric coolers compared to longitudinal coolers with the same figure of merit, providing another motivation in the search for new transverse thermoelectric materials with large figure of merit.