This paper develops universal formulation for a general mixed convection problem in which the solid surface of an isothermal horizontal plate and the ambient fluid are both in motion. Similarity and nonsimilarity equations of six special convection systems can be reduced readily from the universal formulation. Very accurate numerical solutions and comprehensive correlations for 0.01 less-than-or-equal-to Pr less-than-or-equal-to 10 000 are presented over the entire domain of mixed convection and for any relative velocity between the plate and the free stream. The effects of buoyancy and relative velocity on the flow field, temperature field, surface friction, and heat transfer rate are clearly illustrated for a plate moving in parallel or reversely to the free stream for the buoyancy assisting and opposing cases.