The influence of nonstoichiometry on the structural and magnetic properties of \(\hbox {Sr}_2\hbox {FeMoO}_6\) (SFMO) has been investigated by varying the ratio of Fe in polycrystalline samples. We demonstrate that changes in the Fe/Mo ratio can elevate the Curie temperature ( \(T_\textrm{C}\) ) in SFMO, even though the total magnetic moment is reduced at the same time. The discoveries of the stoichiometric imbalance between the cations Fe and Mo are discussed in the context of first-principles calculations on the electronic and magnetic structures of SFMO using the GGA+U method. Our theoretical results reveal that Fe deficiency reduces the \(T_\textrm{C}\) due to the antiparallel alignment of Fe moments in Mo positions, which is consistent with experimental observations. In contrast, accurate \(T_\textrm{C}\) trends for Fe excess are reproduced only by considering spin disorder, with both parallel and antiparallel Fe moment orientations. These insights provide a detailed understanding of the magnetic interactions in SFMO. Our findings lay the groundwork for developing innovative SFMO-based materials and emphasize the significance of stoichiometry control in optimizing SFMO properties.