Cortical dynamics obey a 1/f power law, exhibiting an exponential decay of spectral power with increasing frequency. The slope and offset of this 1/f decay reflect the timescale and magnitude of aperiodic neural activity, respectively. These properties are tightly linked to cellular and circuit mechanisms (e.g. excitation:inhibition balance, firing rates) as well as cognitive processes (perception, memory, state). However, the physiology underlying the 1/f power law in cortical dynamics is not well understood. Here, we compared laminar recordings from human, macaque and mouse cortex to evaluate how 1/f aperiodic dynamics vary across cortical layers and species. We report that 1/f slope is steepest in superficial layers and flattest in deep layers in each species. Additionally, the magnitude of this 1/f decay is greatest in superficial cortex and decreases with depth. Both of these findings can be accounted for by a simple model in which transmembrane currents have longer time constants and greater densities in superficial cortical layers. Together, our results provide novel mechanistic insight into aperiodic dynamics in cortex and suggest that the timescale and magnitude of aperiodic cortical currents decrease with cortical depth.