A theoretical investigation of the relationship between chemical composition and electronic structure was performed on the nonstoichiometric iron sulfide, mackinawite (Fe1+xS), which is isostructural and isoelectronic with the superconducting Fe1+xSe and Fe1+x(Te1-ySey) phases. Even though Fe1+xS has not been measured for superconductivity, the effects of stoichiometry on transport properties and electronic structure in all of these iron-excess chalcogenide compounds has been largely overlooked. In mackinawite, the amount of Fe that has been reported ranges from a large excess, Fe1.15S, to nearly stoichiometric, Fe1.00(7)S. Here, we analyze, for the first time, the electronic structure of Fe1+xS to justify these nonstoichiometric phases. First principles electronic structure calculations using supercells of Fe1+xS yield a wide range of energetically favorable compositions (0 < x < 0.30). The incorporation of interstitial Fe atoms originates from a delicate balance between the Madelung energy and the occupation of Fe-S and Fe-Fe antibonding orbitals. A theoretical assessment of various magnetic structures for "FeS" and Fe1.06S indicate that striped magnetic ordering along [110] is the lowest energy structure and the interstitial Fe affects the values of moments in the square planes as a function of distance. Moreover, the formation of the magnetic moment is dependent on the unit cell volume, thus relating it to composition. Finally, changes in the composition cause a modification of the Fermi surface and ultimately the loss of a nested vector.