One embodiment of the present invention provides a system that estimates the equivalent capacitances for a set of conductors within an electrical structure. During operation, the system constructs a Gaussian surface that encloses a first conductor, but does not contain any other conductor. The system then computes the equivalent capacitance by constructing a sequence of locations within the electric structure, wherein the first location in the sequence is on the Gaussian surface, and the last location in the sequence is on a second conductor in the set of conductors. Specifically, if a location in the sequence of locations is on the surface of a neighboring conductor that is not in the set of conductors, the system can select the next location in the sequence of locations on a neighboring Gaussian surface that encloses the neighboring conductor, but does not contain any other conductor. Note that, by selecting the next location in the sequence of locations on a neighboring Gaussian surface, the system can quickly reach the second conductor, thereby quickly estimating the equivalent capacitance by reducing the computational time required to construct the sequence of locations.