In this note, we announce a complete classification of the stability of periodic roll-wave solutions of the viscous shallow water equations, from their onset at Froude number F approximate to 2 up to the infinite Froude limit. For intermediate Froude numbers, we obtain numerically a particularly simple power-law relation between F and the boundaries of the region of stable periods, which appears potentially useful in hydraulic engineering applications. In the asymptotic regime F. 2(onset), we provide an analytic expression of the stability boundaries, whereas in the limit F ->infinity, we show that roll waves are always unstable. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS. This is an open access article under the CC BY-NC-ND license.