The age of exascale computing has arrived and the risks associated with neutron and other atmospheric radiation are becoming more critical as the computing power increases, hence, the expected Mean Time Between Failures will be reduced because of this radiation. In this work, a new and detailed calculation of the neutron flux for energies above 50 MeV is presented. This has been done by using state-of-the-art Monte Carlo astroparticle techniques and including real atmospheric profiles at each one of the next 23 exascale supercomputing facilities. Atmospheric impact in the flux and seasonal variations were observed and characterised, and the barometric coefficient for high-energy neutrons at each site was obtained. With these coefficients, potential risks of errors associated with the increase in the flux of energetic neutrons, such as the occurrence of single event upsets or transients, and the corresponding failure-in-time rates, can be anticipated just by using the atmospheric pressure before the assignation of resources to critical tasks at each exascale facility. For more clarity, examples about how the rate of failures is affected by the cosmic rays are included, so administrators will better anticipate which more or less restrictive actions could take for overcoming errors.