  Based on a sample of 300 million $K_S$ mesons produced in $\phi \to K_L K_S$
decays recorded by the KLOE experiment at the DA$\Phi$NE $e^+e^-$ collider we
have measured the branching fraction for the decay $K_S \to \pi \mu \nu$. The
$K_S$ mesons are identified by the interaction of $K_L$ mesons in the detector.
The $K_S \to \pi \mu \nu$ decays are selected by a boosted decision tree built
with kinematic variables and by a time-of-flight measurement. Signal
efficiencies are evaluated with data control samples of $K_L \to \pi \mu \nu$
decays. A fit to the reconstructed muon mass distribution finds $7223 \pm 180$
signal events. Normalising to the $K_S \to \pi^+ \pi^-$ decay events the result
for the branching fraction is $\mathcal{B}(K_S \to \pi \mu \nu) = (4.56 \pm
0.11_{\rm stat} \pm 0.17_{\rm syst})\times10^{-4}$.
