Accessing the intrinsic critical current density in type-II superconductors can provide a means to probe microscopic superconducting properties and increase current limits in high-magnetic-field devices and electrical power systems. However, the critical current density measured using direct currents generally lies below this intrinsic limit, mainly because of vortex motion and self-heating. Here we show that picosecond electrical pulses, which act on timescales too short for vortices to move, drive supercurrents up to the intrinsic depairing limit. We probe picosecond critical currents in NbN and YBa2Cu3O7, representative s-wave and d-wave superconductors, respectively. In NbN, we find a sharp onset of the picosecond depairing at a current density of about 2.2 times the conventional critical current density, consistent with microscopic dynamics based on Bardeen–Cooper–Schrieffer theory. By contrast, YBa2Cu3O7 exhibits a gradual suppression of superconductivity with increasing current, reflecting its d-wave symmetry. These results provide a probe of superconductors beyond the reach of conventional transport measurements. Attaining the depairing current could also support superconducting electronics operating closer to intrinsic current limits. Vortex motion and heating prevent direct-current measurements from reaching the intrinsic depairing limit of type-II superconductors. Picosecond pulses bypass these effects and reveal a sharp threshold in NbN but gradual pair breaking in YBa2Cu3O7.