  Using the coherent elastic neutrino-nucleus scattering data of the COHERENT
experiment, we determine for the first time the average neutron rms radius of
$^{133}\text{Cs}$ and $^{127}\text{I}$. We obtain the practically
model-independent value $ R_{n} = 5.5 {}^{+0.9}_{-1.1} \, \text{fm} $ using the
symmetrized Fermi and Helm form factors. We also point out that the COHERENT
data show a $2.3\sigma$ evidence of the nuclear structure suppression of the
full coherence.
