  We have experimentally determined the production rate of $^{39}$Ar and
$^{37}$Ar from cosmic ray neutron interactions in argon at sea level.
Understanding these production rates is important for argon-based dark matter
experiments that plan to utilize argon extracted from deep underground because
it is imperative to know what the ingrowth of $^{39}$Ar will be during the
production, transport, and storage of the underground argon. These measurements
also allow for the prediction of $^{39}$Ar and $^{37}$Ar concentrations in the
atmosphere which can be used to determine the presence of other sources of
these isotopes. Through controlled irradiation with a neutron beam that mimics
the cosmic ray neutron spectrum, followed by direct counting of $^{39}$Ar and
$^{37}$Ar decays with sensitive ultra-low background proportional counters, we
determined that the production rate from cosmic ray neutrons at sea-level is
expected to be $(759 \pm 128)$ atoms/kg$_\text{Ar}$/day for $^{39}$Ar, and
$(51.0 \pm 7.4)$ atoms/kg$_\text{Ar}$/day for $^{37}$Ar. We also performed a
survey of the alternate production mechanisms based on the state-of-knowledge
of the associated cross-sections to obtain a total sea-level cosmic ray
production rate of $(1048 \pm 133)$ atoms/kg$_\text{Ar}$/day for $^{39}$Ar,
$(56.7 \pm 7.5)$ atoms/kg$_\text{Ar}$/day for $^{37}$Ar in underground argon,
and $(92 \pm 13)$ atoms/kg$_\text{Ar}$/day for $^{37}$Ar in atmospheric argon.
