In this paper, we put forward new RCWA algorithms for conical diffractions in a global Cartesian coordinate system. By properly designating signs of electric and magnetic field components and matrix blocks, it is found that boundary conditions can be reduced to exactly the same forms as that of planar diffractions. Conventional stable algorithms like enhanced transmittance matrix or scattering matrix can be spontaneously implemented without any computational violations. This study provides a universal and powerful electromagnetic solver for the fast simulations of stratified periodic nanostructures such as emerging metasurfaces, AR and HUD devices.