  The cut-off effects of the lattice gradient flow -- often called Wilson flow
-- are calculated on a periodic 4-torus at leading order in the gauge coupling.
A large class of discretizations is considered which includes all frequently
used cases in practice. It is shown how the results lead to a smoother
continuum extrapolation for the beta-function of SU(3) gauge theory with N_f =
4 flavors of fermions.
