Based on the discovery of a simple scaling relation, a new technique for the investigation of the phase diagram of nanosized magnetic systems is proposed. By scaling the exchange interaction between magnetic moments, the magnetic phase diagram of currently lithographically produced particles can be obtained from those corresponding to much smaller systems. Such a technique reduces the computation time by several orders of magnitude, and provides a new approach to the investigation of the relative stability of distinct internal magnetic configurations of nanosized systems. The technique is illustrated by the determination of the phase diagram of cylindrically shaped Co particles.