The interaction between itinerant pi and localized d electrons in metal-phthalocyanines, namely, J(pi d) interaction, is considered as responsible for the giant negative magnetoresistance observed in several phthalocyanine-based conductors, among many other important physical properties. Despite the fundamental and technological importance of this on-site intramolecular interaction, its giant ferromagnetic nature has been only recently demonstrated by the experiments conducted by Murakawa et al. in the neutral radical [Fe(Pc)(CN)(2)]-2CHCl(3) (Phys. Rev. B 2015, 92, 054429). In this article, we present the theoretical evaluation of this interaction combining wave function -based electronic calculations on isolated Fe(Pc)(CN)2 molecules and density functional theory -based periodic calculations on the crystal. Our calculations confirm the ferromagnetic nature of the pi-d interaction, with a coupling constant as large as J(pi d)/k(B) = 570 K, in excellent agreement with the experiments, and the presence of intermolecular antiferromagnetic interactions driven by the pi-pi overlap of neighboring phthalocyaninato molecules. The analysis of the wave function of the ground state of the Fe(Pc)(CN)(2) molecule provides the clues of the origin of this giant ferromagnetic pi-d interaction.