The static and dynamic properties of magnetic nanodots with curling in-plane magnetization distribution (vortex) are studied using 3D dynamic micromagnetic simulations. The magnetization distribution, contributions to the total energy, hysteresis behavior, and surface charges are calculated and compared with an analytical vortex model. A phase diagram of the magnetic ground states of magnetic nanodots as a function of the radius and height is calculated and compared with analytical and experimental investigations. The dynamic properties, which are important for high frequency applications, are reported for in-plane and out-of-plane fields.