The active electrical properties of dendrites shape neuronal input and output and are fundamental to brain function. However, our knowledge of active dendrites has been almost entirely acquired from studies of rodents. In this work, we investigated the dendrites of layer 2 and 3 (L2/3) pyramidal neurons of the human cerebral cortex ex vivo. In these neurons, we discovered a class of calcium-mediated dendritic action potentials (dCaAPs) whose waveform and effects on neuronal output have not been previously described. In contrast to typical all-or-none action potentials, dCaAPs were graded; their amplitudes were maximal for threshold-level stimuli but dampened for stronger stimuli. These dCaAPs enabled the dendrites of individual human neocortical pyramidal neurons to classify linearly nonseparable inputs-a computation conventionally thought to require multilayered networks.