A method is outlined for estimating the the average number of synapses forming between cortical neurons as a function of their intercellular separation and the geometry of their dendritic and axonal arborization. Consideration is confined to the formation of local intracortical connections and to the case where the distribution of axonal and dendritic fibres has spherical symmetry. Parameters are deduced from quantitative anatomical studies in murine cortex. It is demonstrated that the majority of local connections forming within a given volume of isotropic cortex can be accounted for on the assumption that local connections between neurons form randomly. From these computations the symmetry of connection between neurons, the likely position for synapse formation on the dendritic tree and the relative synaptic densities attributable to long-and short-range interaction between excitatory and inhibitory neural subsets is determined. Local intracortical couplings appear to be highly asymmetric, and account for about 3200 synapses forming on pyramidal and stellate cells.