The ion saturation current to a spherical probe in the entire range of ion magnetization is computed with SCEPTIC3D, a new three-dimensional version of the kinetic code SCEPTIC designed to study transverse plasma flows. Results are compared with prior two-dimensional calculations valid in the magnetic-free regime (Hutchinson 2002 Plasma Phys. Control. Fusion44 1953), and with recent semi-analytic solutions to the strongly magnetized transverse Mach probe problem (Patacchini and Hutchinson 2009 Phys. Rev. E 80 036403). At intermediate magnetization (ion Larmor radius close to the probe radius) the plasma density profiles show a complex three-dimensional structure that SCEPTIC3D can fully resolve, and, contrary to intuition, the ion current peaks provided the ion temperature is low enough. Our results are conveniently condensed in a single factor Mc, function of ion temperature and magnetic field only, providing the theoretical calibration for a transverse Mach probe with four electrodes placed at 45° to the magnetic field in a plane of flow and magnetic field.