Solid-state nanopores and nanocapillaries find increasing use in a variety of applications including DNA sequencing, synthetic nanopores, next-generation membranes for water purification, and other nanofluidic structures. This paper develops the use of electrochemical impedance spectroscopy to determine the geometry of nanocapillaries. A network equivalent circuit element is derived to include the effects of the capacitive double layer inside the nanocapillaries as well as the influence of varying nanocapillary radius. This variable topology function is similar to the finite Warburg impedance in certain limits. Analytical expressions for several different nanocapillary shapes are derived. The functions are evaluated to determine how the impedance signals will change with different nanocapillary aspect ratios and different degrees of constriction or inflation at the capillary center. Next, the complex impedance spectrum of a nanocapillary array membrane is measured at varying concentrations of electrolyte to separate the effects of nanocapillary double layer capacitance from those of nanocapillary geometry. The variable topology equivalent circuit element model of the nanocapillary is used in an equivalent circuit model that included contributions from the membrane and the measurement apparatus. The resulting values are consistent with the manufacturer's specified tolerances of the nanocapillary geometry. It is demonstrated that electrochemical impedance spectroscopy can be used as a tool for in situ determination of the geometry of nanocapillaries.