A 3D eddy current formulation based on constrained eddy currents and direct inclusion of the velocity terms is presented. Velocity terms in all three dimensions can be accommodated, although only two velocity components are normally needed and often one velocity term is sufficient. The inclusion of all three terms allows modeling of velocity terms that are not parallel to element sides. The eddy currents as well as induced currents through velocity are constrained by enforcing the continuity equation. Results for a moving coil over a conductor are presented as an example for the use of this method. >