To quantitatively evaluate the formation energies of the (N–N)_As/(N–As)_As/(As–As)_As split interstitials in dilute GaAsN alloys, first-principles total-energy calculations using a projector augmented wave method are performed. The formation energies for different defects are calculated as a function of the atomic chemical potentials of constituent elements. We compare the formation energies for the N_As substitution and split interstitial complexes based on the traditional (100) and high-index GaAs (311) A/B plane under Ga-rich and As-rich conditions. According to the results of comparison, the chemical potential condition of forming-related defect and the dominant defect for all planes are determined.