  The general features of the neutrino flux from cosmic ray interactions in the
Earth's atmosphere are well characterized. However, the absolute precision of
calculations is still insufficient and the uncertainty from the modeling of
hadronic interactions in the very forward region remains a major limitation. In
this work, we benchmark the current generation hadronic models using
high-precision atmospheric muon calculations from a few GeV to multiple TeV
energies provided by the MCEq code. We derive corrections to hadronic models
using publicly available measurements of the flux and charge ratio of
atmospheric muons from surface and underground detectors. When combining data,
the experimental uncertainties are taken into account. We discuss the
calibration method and the strength of the derived constraints.
