In 1986, electron microscopy was used to reconstruct by hand the entire nervous system of a roundworm, the nematode Caenorhabditis elegans1. Since this landmark study, high-throughput electron-microscopic techniques have enabled reconstructions of much larger mammalian brain circuits at synaptic resolution2,3. Nevertheless, it remains unknown how the structure of a synapse relates to its physiological transmission strength-a key limitation for inferring brain function from neuronal wiring diagrams. Here we combine slice electrophysiology of synaptically connected pyramidal neurons in the mouse somatosensory cortex with correlated light microscopy and high-resolution electron microscopy of all putative synaptic contacts between the recorded neurons. We find a linear relationship between synapse size and strength, providing the missing link in assigning physiological weights to synapses reconstructed from electron microscopy. Quantal analysis also reveals that synapses contain at least 2.7 neurotransmitter-release sites on average. This challenges existing release models and provides further evidence that neocortical synapses operate with multivesicular release4-6, suggesting that they are more complex computational devices than thought, and therefore expanding the computational power of the canonical cortical microcircuitry.