Atmospheric immersion freezing (IF), a heterogeneous ice nucleation process where an ice nucleating particle (INP) is immersed in supercooled water, is a dominant ice formation pathway impacting the hydrological cycle and climate. Implementation of IF derived from field and laboratory data in cloud and climate models is difficult due to the high variability in spatio-temporal scales, INP composition, and morphological complexity. We demonstrate that IF can be consistently described by a stochastic nucleation process accounting for uncertainties in the INP surface area. This approach accounts for time-dependent freezing, a wide range of surface areas and challenges phenomenological descriptions typically used to interpret IF. The results have an immediate impact on the current description, interpretation, and experiments of IF and its implementation in models. The findings are in accord with nucleation theory, and thus should hold for any supercooled liquid material that nucleates in contact with a substrate.