  The atmospheres of cool stars are temporally and spatially inhomogeneous due
to the effects of convection.The influence of this inhomogeneity, referred to
as granulation, on colours has never been investigated over a large range of
effective temperatures and gravities. We aim to study, in a quantitative way,
the impact of granulation on colours. We use the CIFIST grid of CO5BOLD
hydrodynamical models to compute emerging fluxes. These in turn are used to
compute theoretical colours in the UBVRI,2MASS,Hipparcos,Gaia and SDSS systems.
Every CO5BOLD model has a corresponding one dimensional (1D) plane-parallel LHD
model computed for the same atmospheric parameters, which we used to define a
"3D correction" that can be applied to colours computed from fluxes computed
from any 1D model atmosphere code. The 3D corrections on colours are generally
small, of the order of a few hundredths of a magnitude, yet they are far from
negligible. We find that ignoring granulation effects can lead to
underestimation of Teff by up to 200K and overestimation of gravity by up to
0.5dex, when using colours as diagnostics. We have identified a major
shortcoming in how scattering is treated in the current version of the CIFIST
grid, which could lead to offsets of the order 0.01mag, especially for colours
involving blue and UV bands.We have investigated the Gaia and Hipparcos
photometric systems and found that the (G-H_p),(BP-RP) diagram is immune to the
effects of granulation. In addition, we point to the potential of the RVS
photometry as a metallicity diagnostic. Our investigation shows that the
effects of granulation should not be neglected if one wants to use colours as
diagnostics of the stellar parameters of F,G,K stars. A limitation is that
scattering is treated as true absorption in our current computations, thus our
3D corrections are likely an upper limit to the true effect. (Abridged)
