Under current conditions, the cosmic ray spectrum incident on the Earth is dominated by particles with energies < 1 GeV. Astrophysical sources including high energy solar flares, supernovae and gamma ray bursts produce high energy cosmic rays (HECRs) with drastically higher energies. The Earth is likely episodically exposed to a greatly increased HECR flux from such events, some of which lasting thousands to millions of years. The air showers produced by HECRs ionize the atmosphere and produce harmful secondary particles such as muons and neutrons. Neutrons currently contribute a significant radiation dose at commercial passenger airplane altitude. With higher cosmic ray energies, these effects will be propagated to ground level. This work shows the results of Monte Carlo simulations quantifying the neutron flux due to high energy cosmic rays at various primary energies and altitudes. We provide here lookup tables that can be used to determine neutron fluxes from primaries with total energies 1 GeV - 1 PeV. By convolution, one can compute the neutron flux for any arbitrary CR spectrum. Our results demonstrate that deducing the nature of primaries from ground level neutron enhancements would be very difficult.