This study demonstrates an analytical relation that models the carrier injection in metal-organic interfaces and which considers two consecutive carriers hopping as the injection mechanism. The new formula has superior attributes and can surpass conventional relations, in particular the thermionic emission-diffusion formula. For example, the model can properly trace the temperature dependency of the injection up to temperatures as low as 30 K and the full range of electric fields. Also, the prominence of joule heating for proper modeling of the injection is presented. This study examines the validity of the introduced analytical equation by exploring the injection in several practical contacts extracted from the literature, the results of which are discussed in this paper.