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)
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