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 H_SW 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 ΔE 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.