  Spectroscopic measurements of iron abundances are prone to systematic
modelling errors. We present 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 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 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 low excitation potential. The corresponding abundance differences
between 3D non-LTE and 1D non-LTE are generally less severe but can still reach
$\pm$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 remove excitation imbalances that amount to 250 K to 300 K errors in
effective temperature. For Procyon, the 3D non-LTE models suggest [Fe/H] = 0.11
$\pm$ 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.
