The homogeneous freezing of water is of fundamental importance to a number of fields, including that of cloud formation. However, there is considerable scatter in homogeneous nucleation rate coefficients reported in the literature. Using a cold stage droplet system designed to minimize uncertainties in temperature measurements, we examined the freezing of over 1500 pure water droplets with diameters between 4 and 24 mu m. Under the assumption that nucleation occurs within the bulk of the droplet, nucleation rate coefficients fall within the spread of literature data and are in good agreement with a subset of more recent measurements. To quantify the relative importance of surface and volume nucleation in our experiments, where droplets are supported by a hydrophobic surface and surrounded by oil, comparison of droplets with different surface area to volume ratios was performed. From our experiments it is shown that in droplets larger than 6 mu m diameter (between 234.6 and 236.5 K), nucleation in the interior is more important than nucleation at the surface. At smaller sizes we cannot rule out a significant contribution of surface nucleation, and in order to further constrain surface nucleation, experiments with smaller droplets are necessary. Nevertheless, in our experiments, it is dominantly volume nucleation controlling the observed nucleation rate.