Abstract: Quantitative modelling of precipitation kinetics can play an important role in a computational material design framework where, for example, optimization of alloying can become more efficient if it is computationally driven. Precipitation hardening (PH) stainless steels is one example where precipitation strengthening is vital to achieve optimum properties. The Langer–Schwartz–Kampmann–Wagner (LSKW) approach for modelling of precipitation has shown good results for different alloy systems, but the specific models and assumptions applied are critical. In the present work, we thus apply two state-of-the-art LSKW tools to evaluate the different treatments of nucleation and growth. The precipitation modelling is assessed with respect to experimental results for Cu precipitation in PH stainless steels. The LSKW modelling is able to predict the precipitation during ageing in good quantitative agreement with experimental results if the nucleation model allows for nucleation of precipitates with a composition far from the equilibrium and if a composition-dependent interfacial energy is considered. The modelling can also accurately predict trends with respect to alloy composition and ageing temperature found in the experimental data. For materials design purposes, it is though proposed that the modelling is calibrated by measurements of precipitate composition and fraction in key experiments prior to application. Graphic abstract: [Figure not available: see fulltext.].