Contrail–cirrus is probably the largest climate forcing from aviation. The evolution of contrail–cirrus and its radiative impact depends not only on a multitude of atmospheric parameters, but also on the geometric and microphysical properties of the young contrails evolving into contrail–cirrus. The early evolution of contrails (t  <  5 min) is dominated by an interplay of ice microphysics and wake vortex dynamics. Young contrails may undergo a fast vertical expansion due to a descent of the wake vortices and may lose a substantial fraction of their ice crystals due to adiabatic heating. The geometric depth H and total ice crystal number N of young contrails are highly variable and depend on many environmental and aircraft parameters. Both properties, H and N, affect the later properties of the evolving contrail–cirrus, as they control the extent of shear-induced spreading and sedimentation losses. In this study, we provide parametrisations of H and N after 5 min taking into account the effects of temperature, relative humidity, thermal stratification and aircraft type (mass, wing span, fuel burn). The parametrisations rely on a large data set of recent large-eddy simulations of young contrails. They are suited to be incorporated in larger-scale models in order to refine the present-day contrail initialisations by considering the processes that strongly affect the contrail evolution during the vortex phase.