An outstanding challenging in nanomagnetism is the quantitative understanding of magnetization reversal process of nanostructures. We investigate the magnetization reversal of individual Co islands on Cu(111). We measure switching fields HSW of single Co islands using spin-polarized scanning tunneling microscopy/spectroscopy at 8 K. The switching field changes with island size. The switching field increases with size and reaches a maximum value of 2.4 T at a size of 5500 atoms, and decreases for larger islands. To discuss magnetization reversal processes, we extract the energy barrier ∆E for magnetization reversal as a function of island size. Our analysis reveals a crossover of the magnetization reversal from an exchange-spring behavior to domain wall formation with increasing size at around 7500 atoms.