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Cosmic rays, high-energy subatomic particles of extraterrestrial origin, are systematically measured by space-borne and ground-based instruments. A specific interest is paid to high-energy ions accelerated during solar eruptions, so-called solar energetic particles. In order to build a comprehensive picture of their nature, it is important to fill the gap and inter-calibrate ground-based and space-borne instruments. Here, we focus on ground-based detectors, specifically neutron monitors, which form a global network and provide continuous recording of cosmic ray intensity and its variability, used also to register relativistic solar energetic particles. The count rate of each neutron monitor is determined by the geomagnetic and atmospheric cut-offs, both being functions of the location. Here, on the basis of Monte Carlo simulations with the PLANETOCOSMICS code and by the employment of a new verified neutron monitor yield function, we assessed the atmospheric cut-off as a function of the altitude, as well as for specific stations located in the polar region. The assessed in this study altitude profile of the atmospheric cut-off for primary cosmic rays builds the basis for the joint analysis of strong solar proton events with different instruments and allows one to clarify recent definitions and related discussions about the new sub-class of events, so-called sub-ground-level enhancements (sub-GLEs).