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A two-dimensional numerical approach for calculating capacitance between two conductors through different dielectrics is developed. The approach uses Laplace's equation in two dimensions to determine potentials on a grid system between the conductors. Equipotential lines are generated using these potentials and curvilinear squares can be formed to construct the flux tubes between the conductors. The application of Gauss's law to these potentials provides the charge on a conductor and results in the determination of capacitance values.