Novel method to calculate flux linkage for 3-D finite element analysis is proposed. It does not require any integral path if the current direction in a coil is known. The flux linkage can be calculated very easily using simple volume based integration. The current direction is calculated based on the recently developed technique by the authors. The novel method for flux linkage calculation is verified by applying to a very complicated deflection yoke coil. The simulation result is compared to the experimental one. From the simulation, it is shown that the proposed method is very accurate and effective to calculate the flux linkage of a coil.