Dendritic spines are the nearly ubiquitous site of excitatory synaptic input onto neurons and as such are critically positioned to influence diverse aspects of neuronal signalling. Decades of theoretical studies have proposed that spines may function as highly effective and modifiable chemical and electrical compartments that regulate synaptic efficacy, integration and plasticity. Experimental studies have confirmed activity-dependent structural dynamics and biochemical compartmentalization by spines. However, there is a longstanding debate over the influence of spines on the electrical aspects of synaptic transmission and dendritic operation. Here we measure the amplitude ratio of spine head to parent dendrite voltage across a range of dendritic compartments and calculate the associated spine neck resistance (R(neck)) for spines at apical trunk dendrites in rat hippocampal CA1 pyramidal neurons. We find that R(neck) is large enough (~500 MΩ) to amplify substantially the spine head depolarization associated with a unitary synaptic input by ~1.5- to ~45-fold, depending on parent dendritic impedance. A morphologically realistic compartmental model capable of reproducing the observed spatial profile of the amplitude ratio indicates that spines provide a consistently high-impedance input structure throughout the dendritic arborization. Finally, we demonstrate that the amplification produced by spines encourages electrical interaction among coactive inputs through an R(neck)-dependent increase in spine head voltage-gated conductance activation. We conclude that the electrical properties of spines promote nonlinear dendritic processing and associated forms of plasticity and storage, thus fundamentally enhancing the computational capabilities of neurons.