Hydrogen combustion is gaining attention for its potential to enable low-emission energy conversion in gas turbines. Since hydrogen is carbon-free, it produces no carbon-based pollutants and primarily forms water vapor. However, due to its higher adiabatic flame temperature with respect to hydrocarbons, hydrogen combustion is more prone to increased nitrogen oxides (NOx[jls-end-space/]) formation. Accurately predicting NOx formation remains a major challenge, particularly when scaling from laboratory experiments to industrial applications. While scaling laws are widely used in fluid dynamics, their application to NOx emissions is challenging due to the complex nature of NOx formation. This study develops a semi-empirical, physics-based correlation to estimate NOx emissions in swirl-stabilized, partially premixed lean hydrogen–air burners. The proposed correlation expresses the Emission Index of NOx (EINOx[jls-end-space/]) as a function of key operating and design parameters, including fuel mass flow rate, pressure, adiabatic flame temperature, equivalence ratio, residence time and swirl number. It builds upon Westenberg’s NOx formation rate equation, incorporating composition-dependent effects via equivalence ratio. The slow formation nature of NOx is accounted for via the combustor mean residence time. Additionally, the influence of swirl on the mixing process is modeled through a swirl-modified effective equivalence ratio, acknowledging that while partial premixing is a design choice, swirl intensity can either enhance or disrupt the degree of premixing before combustion. The model’s parameters were calibrated using experimental data from published literature. By providing a predictive tool for NOx scaling across different operating conditions, this model supports the development and design of experiments and devices for hydrogen–air combustion.