Iron is one of the most important elements in-stellar astrophysics. However, spectroscopic measurements of its abundance are prone to systematic modelling errors. We present three dimensional non-local thermodynamic equilibrium (3D non-LTE) calculations across 32 STAGGER-grid models with effective temperatures from 5000 K to 6500 K, surface gravities of 4.0 dex and 4.5 dex, and metallicities from −3 dex to 0 dex, and we study the effects on 171 Fe I and 12 Fe II optical lines. In warm metal-poor stars, the 3D non-LTE abundances are up to 0.5 dex larger than 1D LTE abundances inferred from Fe I lines of an intermediate excitation potential. In contrast, the 3D non-LTE abundances can be 0.2 dex smaller in cool metal-poor stars when using Fe I lines of a low excitation potential. The corresponding abundance differences between 3D non-LTE and 1D non-LTE are generally less severe but can still reach ±0.2 dex. For Fe II lines, the 3D abundances range from up to 0.15 dex larger to 0.10 dex smaller than 1D abundances, with negligible departures from 3D LTE except for the warmest stars at the lowest metallicities. The results were used to correct 1D LTE abundances of the Sun and Procyon (HD 61421), and of the metal-poor stars HD 84937 and HD 140283, using an interpolation routine based on neural networks. The 3D non-LTE models achieve an improved ionisation balance in all four stars. In the two metal-poor stars, they removed excitation imbalances amounting to 250 K to 300 K errors in effective temperature. For Procyon, the 3D non-LTE models suggest [Fe/H] = 0.11 ± 0.03, which is significantly larger than literature values based on simpler models. We make the 3D non-LTE interpolation routine for FG-type dwarfs publicly available, in addition to 1D non-LTE departure coefficients for standard MARCS models of FGKM-type dwarfs and giants. These tools, together with an extended 3D LTE grid for Fe II from 2019, can help improve the accuracy of stellar parameter and iron abundance determinations for late-type stars.