Synapses between neurons control the the strengths of neuronal communication in neural circuits and their strengths are in turn dynamically regulated by experience. Because dendritic spine head volumes are highly correlated synaptic strength [1], anatomical reconstructions can probe the distributions of synaptic strengths. Synapses from the same axon onto the same dendrite (SDSA pairs) have a common history of coactivation and have nearly the same spine head volumes, suggesting that synapse function precisely modulates structure. We have applied Shannon information theory to obtain a new analysis of synaptic information storage capacity (SISC) using non-overlapping clusters of dendritic spine head volumes as a measure of synaptic strengths with distinct states based on the synaptic precision level calculated from 10 SDSA pairs. SISC analysis revealed spine head volumes in the stratum radiatum of hippocampal area CA1 occupied 24 distinct states (4.1 bits). This finding indicates an unexpected degree of precision that has implications for learning algorithms in artificial neural network models.