  Stochastic gravitational wave backgrounds, predicted in many models of the
early universe and also generated by various astrophysical processes, are a
powerful probe of the Universe. The spectral shape is key information to
distinguish the origin of the background since different production mechanisms
predict different shapes of the spectrum. In this paper, we investigate how
precisely future gravitational wave detectors can determine the spectral shape
using single and broken power-law templates. We consider the detector network
of Advanced-LIGO, Advanced-Virgo and KAGRA and the space-based
gravitational-wave detector DECIGO, and estimate the parameter space which
could be explored by these detectors. We find that, when the spectrum changes
its slope in the frequency range of the sensitivity, the broken power-law
templates dramatically improve the $\chi^2$ fit compared with the single
power-law templates and help to measure the shape with a good precision.
