Heterogeneous nucleation is a phenomenon that starts the condensation of supersaturated vapours on solid surfaces. An example is the formation of cirrus clouds in the atmosphere: their formation is often triggered at relative humidities clearly above 100%. We derive a new theory that can be used to calculate the threshold supersaturation of heterogeneous nucleation of water vapour on nanoparticles and show that it performs significantly better than older theories when compared to lab experiment.