Copper electroplating is widely used to fabricate Large-Scale Integration (LSI) whose components are from nanoscale wires to microscale bumps because of its excellent via/trench filling ability, good adhesion and lower process temperature and low cost. Monitoring and controlling current densities on a plated surface are necessary to electroplate the object optimally. This paper focuses on monitoring the current densities on a plated surface and a novel technique to estimate them from the electric potentials in the plating cell has been developed. An electric potential at a point can be measured by using a capillary inserted in the cell. Evaluation of a physical quantity on a boundary from known values in the domain is an inverse problem. In the present method, Tikhonov regularization on the mathematical model of the electric field derived by boundary element method is applied to solve the inverse problem. In addition, the method plots polarization curves which describe the relationships between electric potentials and current destinies on the boundaries with the inverse solutions and revises the solutions. Measurement experiments under several electroplating conditions were performed to demonstrate the validity of the proposed technique. The estimation results by the proposed method are in good agreement with the numerical results by the conventional method using sample polarization curves. These results show that this method can be applied to practical electroplating processes in LSI fabrications.