We have calculated the global distribution of atmospheric neutrons and their products by a Monte Carlo simulation of nucleon transport, in the internuclear cascade followed by neutron transport below 19 Mev. First, we present the results generated by monoenergetic primary protons and alpha particles entering the top of the atmosphere. Second, the kernels derived from the monoenergetic cases are used to determine the spatial and energy distributions of neutrons and their products from the protons and alpha particles in the cosmic radiation; solar modulation effects are included. The calculation is compared, in the 1‐ to 10‐Mev region, with the results of our fast neutron experiment; the agreement is within the uncertainties of the primary spectrum and of the experimental results over most of the atmosphere. The calculation is then normalized to the experiment in the fast neutron region. The results of the normalized calculation include the steady state neutron spectrum, the neutron production rates, the radiocarbon production rates, the neutron leakage rates from the top of the atmosphere, and the production rates of other nuclides. The normalized calculation reproduces experimentally observed slow neutron densities and the observed neutron flux and spectrum above 1 kev, and it predicts features of the atmospheric neutron morphology not yet observed. The points of agreement and divergence with earlier calculations are discussed, including the radiocarbon production rates and the neutron leakage rates during solar cycle 20, which is near the mean of the last 10 solar cycles.