Homogeneous nucleation rates are determined for micrometer sized water droplets levitated inside an electrodynamic Paul-trap. The size of a single droplet is continuously measured by analyzing the angle-resolved light scattering pattern of the droplets with classical Mie theory. The freezing process is detected by a pronounced increase in the depolarization of the scattered light. By statistical analysis of the freezing process of some thousand individual droplets, we obtained the homogeneous nucleation rate of water between 236 and 237 K. The values are in agreement with former expansion cloud chamber measurements but could be determined with considerably higher precision. The measurements are discussed in the light of classical nucleation theory in order to obtain the size and the formation energy of the critical nucleus.