Thirty-four years since the small nervous system of the nematode C. elegans was manually reconstructed in the electron microscope (EM) 1 , 'high-throughput' EM techniques now enable the dense reconstruction of neural circuits within increasingly large brain volumes at synaptic resolution [2][3][4][5][6] . As with C. elegans, however, a key limitation for inferring brain function from neuronal wiring diagrams is that it remains unknown how the structure of a synapse seen in EM relates to its physiological transmission strength. Here, we related structure and function of the same synapses to bridge this gap: we combined paired whole-cell recordings of synaptically connected pyramidal neurons in slices of mouse somatosensory cortex with correlated light microscopy and high-resolution EM of all putative synaptic contacts between the neurons. We discovered a linear relationship between synapse size (postsynaptic density area) and synapse strength (excitatory postsynaptic potential amplitude), which provides an experimental foundation for assigning the actual physiological weights to synaptic connections seen in the EM. Furthermore, quantal analysis revealed that the number of vesicle release sites exceeded the number of anatomical synapses formed by a connection by a factor of at least 2.6, which challenges the current understanding of synaptic release in neocortex and suggests that neocortical synapses operate with multivesicular release, like hippocampal synapses [7][8][9][10][11] . Thus, neocortical synapses are more complex computational devices and may modulate their strength more flexibly than previously thought, with the corollary that the canonical neocortical microcircuitry possesses significantly higher computational power than estimated by current models.