Chemical equilibrium for gives
after neglecting the ion--atom mass difference in the translational prefactor.
Because equilibrium reactions balance chemical potentials and photons have zero chemical potential,
The rest-mass difference in the Maxwell--Boltzmann densities then supplies the Boltzmann factor .
For , the hydrogen binding energy is the rest-energy defect

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The Saha ionization equation is a mathematical formula that describes the ratio of the number densities of ions to neutral atoms in a thermal equilibrium state, particularly in astrophysical contexts such as stellar atmospheres. It is useful for understanding how ionization states of elements vary with temperature and electron pressure.