Rigorous coupled-wave analysis (RCWA) has become one of the most efficient electromagnetic solvers to cope with the diffractions of large-scale periodic nanostructures. Conventional RCWAs focus on planar diffractions and their iterative stabilities. Conical diffractions, as more general incidence cases, are paid little attention in developing their universal and stable implementations for multilayered gratings. Here, we reformulate RCWA algorithms step by step for conical diffractions in a global Cartesian coordinate system. By applying some mathematics tricks, it is found that boundary conditions in conical diffractions can be reduced to the same forms as that of planar diffractions. Conventional stable algorithms including enhanced transmittance matrices and scattering matrices can be directly implemented to attain robust diffraction efficiencies as well as electromagnetic fields for multilayered gratings. An exemplary application in diffractive-waveguide-based augmented reality verified our algorithms.