  We derive a full analytical approximation to the stochastic gravitational
wave background generated by the loops that are produced throughout the
cosmological evolution of cosmic string networks. We show that this
approximation not only predicts the amplitude of the radiation-era plateau
exactly, but also provides a good fit to the high-frequency cut-off and to the
low-frequency peak generated by the loops that decay during the matter era,
irrespective of cosmic string tension and of the length of loops created. We
then find that it provides a good quantitative description of the full
stochastic gravitational wave background across the relevant frequency range.
