The fluctuations of the charge on an electrode contain information on the microscopic correlations within the adjacent fluid and their effect on the electronic properties of the interface. We investigate these fluctuations using molecular dynamics simulations in a constant-potential ensemble with histogram reweighting techniques. This approach offers in particular an efficient, accurate and physically insightful route to the differential capacitance that is broadly applicable. We demonstrate these methods with three different capacitors: pure water between platinum electrodes, and a pure as well as a solvent-based organic electrolyte each between graphite electrodes. The total charge distributions with the pure solvent and solvent-based electrolytes are remarkably Gaussian, while in the pure ionic liquid the total charge distribution displays distinct non-Gaussian features, suggesting significant potential-driven changes in the organization of the interfacial fluid.