Two different methods to calculate the steady-state nucleation rate in heteromolecular systems proposed by Stauffer (1976) and Langer (1969) are analyzed. Their mathematical equivalence is explicitly demonstrated, thereby obtaining a generic expression for the rate of binary nucleation. Its numerical evaluation does not entail rotation of the coordinate system at the saddle point, but it only requires data in the natural coordinate system of number fluctuations, namely molecular impingement rates, the droplet free energy and its second order derivatives at the saddle point, and the total density of condensible vapors.