Older GCE models predict [K/Fe] ratios as much as 1 dex lower than those inferred from stellar observations. Abundances of potassium are mainly based on analyses of the 7698 $AA$ resonance line, and the discrepancy between models and observations is in part caused by the LTE assumption. We study the statistical equilibrium of KI, focusing on the non-LTE effects on the $7698 AA$ line. We aim to determine how non-LTE abundances of K can improve the analysis of its chemical evolution, and help to constrain the yields of models. We construct a model atom that employs the most up-to-date data. In particular, we calculate and present inelastic e+K collisional excitation cross-sections from the convergent close-coupling and the $B$-Spline $R$-matrix methods, and H+K collisions from the two-electron model. We constructed a fine grid of non-LTE abundance corrections that span $4000<teff / rm{K}<8000$, $0.50<lgg<5.00$, $-5.00<feh<+0.50$, and applied the corrections to abundances from the literature. In concordance with previous studies, we find severe non-LTE effects in the $7698 AA$ line, which is stronger in non-LTE with abundance corrections that can reach $sim-0.7,dex$. We explore the effects of atmospheric inhomogeneity by computing a full 3D non-LTE stellar spectrum of KI for a test star. We find that 3D is necessary to predict a correct shape of the resonance 7698 $AA$ line, but the line strength is similar to that found in 1D non-LTE. Our non-LTE abundance corrections reduce the scatter and change the cosmic trends of literature K abundances. In the regime [Fe/H]$lesssim-1.0$ the non-LTE abundances show a good agreement with the GCE model with yields from rotating massive stars. The reduced scatter of the non-LTE corrected abundances of a sample of solar twins shows that line-by-line differential analysis techniques cannot fully compensate for systematic modelling errors.
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