The distribution of nitrogen isotopes in the biosphere has the potential to offer insights into the past, present and future of the nitrogen cycle, but it is challenging to unravel the processes controlling patterns of mixing and fractionation. We present a mathematical model describing a previously overlooked process: nitrogen isotope fractionation during leaf-atmosphere NH3(g) exchange. The model predicts that when leaf-atmosphere exchange of NH3(g) occurs in a closed system, the atmospheric reservoir of NH3(g) equilibrates at a concentration equal to the ammonia compensation point and an isotopic composition 8.1‰ lighter than nitrogen in protein. In an open system, when atmospheric concentrations of NH3(g) fall below or rise above the compensation point, protein can be isotopically enriched by net efflux of NH3(g) or depleted by net uptake. Comparison of model output with existing measurements in the literature suggests that this process contributes to variation in the isotopic composition of nitrogen in plants as well as NH3(g) in the atmosphere, and should be considered in future analyses of nitrogen isotope circulation. The matrix-based modelling approach that is introduced may be useful for quantifying isotope dynamics in other complex systems that can be described by first-order kinetics.