The universal criterion for ultrafast vortex-core switching between the up- and down-core bistates in soft magnetic nanodots was investigated by micromagnetic simulations along with analytical calculations. Vortex-core switching occurs whenever the velocity of vortex-core motion reaches the critical velocity that is expressed as (e.g. m/s for Permalloy), where Aex is the exchange stiffness, and is the gyromagnetic ratio. On the basis of the above results, phase diagrams for the vortex-core switching event and switching times with respect to both the amplitude and frequency of applied circularly rotating magnetic field were calculated, which offer practical guidance for implementing nanodots in vortex states into future solid-state information-storage devices.