  Particles count rates at given Earth location and altitude result from the
convolution of (i) the interstellar (IS) cosmic-ray fluxes outside the solar
cavity, (ii) the time-dependent modulation of IS into Top-of-Atmosphere (TOA)
fluxes, (iii) the rigidity cut-off (or geomagnetic transmission function) and
grammage at the counter location, (iv) the atmosphere response to incoming TOA
cosmic rays (shower development), and (v) the counter response to the various
particles/energies in the shower. Count rates from neutron monitors or muon
counters are therefore a proxy to solar activity. In this paper, we review all
ingredients, discuss how their uncertainties impact count rate calculations,
and how they translate into variation/uncertainties on the level of solar
modulation $\varphi$ (in the simple Force-Field approximation). The main
uncertainty for neutron monitors is related to the yield function. However,
many other effects have a significant impact, at the 5-10\% level on $\varphi$
values. We find no clear ranking of the dominant effects, as some depend on the
station position and/or the weather and/or the season. An abacus to translate
any variation of count rates (for neutron and $\mu$ detectors) to a variation
of the solar modulation $\varphi$ is provided.
