The purpose of this study was to parametrize the in-air one sigma spot size for various energies and air gaps in pencil beam scanning (PBS) proton therapy. The current study included range shifters with a water equivalent thickness (WET) of 40��mm (RS40) and 75��mm (RS75). For RS40, the spot sizes were measured for energies ranging from 80 to 225��MeV in increments of 2.5��MeV, whereas the air gap was varied from 5 to 25��cm in increments of 2.5��cm. For RS75, the spot sizes were measured for energies ranging from 120 to 225��MeV in increments of 2.5��MeV, whereas the air gap was varied from 5 to 35��cm in increments of 2.5��cm. For both RS40 and RS75, all measurements (n = 1090) were acquired at the isocenter using a Lynx 2D scintillation detector. For RS40, the spot sizes increased from 3.1��mm to 10.4��mm, whereas the variation in spot sizes for RS75 ranged from 3.3��mm to 13.1��mm. For each range shifter, an analytical equation demonstrating the relationship of the spot size with the proton energy and air gap was obtained. The best parametrization results were obtained with the 3rd degree polynomial fits of the energy and air gap parameters. The average difference between the modeled and measured spot sizes was 0.0 �� 0.1��mm (range, �����0.24���0.21��mm) for RS40, and 0.0 �� 0.1��mm (range, �����0.23���0.15��mm) for RS75. In conclusion, the analytical model agrees within �� 0.25��mm of the measured spot sizes on a ProteusPLUS PBS proton system with a PBS dedicated nozzle.