We investigate NLTE effects for magnesium and calcium in the atmospheres of late-type giant and supergiant stars .
The aim of this paper is to provide a grid of NLTE/LTE equivalent width ratios W / W ^ { * } of Mg and Ca lines for the following range of stellar parameters : T _ { eff } \in [ 3500 , 5250 ] K , \log g \in [ 0.5 , 2.0 ] dex and [ Fe/H ] \in [ -4.0 , 0.5 ] dex .
We use realistic model atoms with the best physics available and taking into account the fine structure .
The Mg and Ca lines of interest are in optical and near IR ranges .
A special interest concerns the lines in the Gaia spectrograph ( RVS ) wavelength domain [ 8470 , 8740 ] Å .
The NLTE corrections are provided as function of stellar parameters in an electronic table as well as in a polynomial form for the Gaia /RVS lines .