Sea surface roughness is affected by surface current gradients, which provides a means of monitoring from satellite sharp oceanic fronts. This paper is the second report of an experiment designed to compare observations of sea surface roughness and surface currents at an unprecedented accuracy, owing to the conjunction of numerous deployed drifters and roughness instruments. About 200 drifters sampled a thin 10 km elongated submesoscale front, also monitored by a high density of roughness instruments: satellite synthetic aperture radar, satellite, and airborne multiangle sunglint radiometers. The first paper focused on the retrieval of the current gradient direction (convergence and cyclonic vorticity) at the front, using roughness observations at multiple angle from airplane. This second paper focuses on the retrieval of the current gradient magnitude and scale, using roughness observations at different scales, from airplane and from satellite. Two main results are obtained: (i) Trajectories of selected drifters show that the front is only 50 m wide and unambiguously exhibits convergence and cyclonic vorticity up to 100f (with f the Coriolis frequency). This far exceeds previously documented values for submesoscale deep ocean fronts. (ii) Correct estimation of such extreme current gradients using surface roughness hinges on instruments with sufficiently high spatial resolution. Lower‐resolution roughness sensors can still detect the front, as demonstrated from observations and a simplified model, but cannot properly estimate the current gradient magnitude and the frontal width. Those results provide guidelines for monitoring intense current gradients from space using sea surface roughness.