Eight spinel-group minerals were synthesized by a flux-growth method producing spinels with varying composition and Fe3+/Fetot ratios. The mean force constants of iron bonds in these minerals were determined by synchrotron nuclear resonant inelastic X-ray scattering (NRIXS) in order to determine the reduced isotopic partition function ratios (β-factors) of these spinels. The mean force constants are strongly dependent on the Fe3+/Fetot of the spinel but are independent, or weakly dependent on other structural and compositional parameters. From our spectroscopic data, it is found that a single redox-dependent calibration line accounts for the effects of Fe3+/Fetot on the β-factors of spinels. This calibration successfully describes the equilibrium Fe isotopes fractionation factors between spinels and silicates (olivine and pyroxenes). Our predictions are in excellent agreement with independent determinations for the equilibrium Fe isotopic fractionations for the magnetite-fayalite and the magnetite-hedenbergite couples. Our calibration applies to the entire range of Fe3+/Fetot ratios found in natural spinels and provides a basis for interpreting iron isotopic variations documented in mantle peridotites. Except for a few exceptions, most of the samples measured so far are in isotopic disequilibrium, reflecting metasomatism and partial melting processes.