We present a theoretical model for the non-thermal radio emission from single hot stars, in terms of synchrotron radiation from electrons accelerated in wind-embedded shocks. The model is described by five independent parameters each with a straightforward physical interpretation. Applying the model to a high-quality observation of Cyg OB2 No. 9 (O5 If), we obtain meaningful constraints on most parameters. The most important result is that the outer boundary of the synchrotron emission region must lie between 500 and 2200 stellar radii. This means that shocks must persist up to that distance. We also find that relatively weak shocks (with a compression ratio