Many experiments with slow counting rates are limited by the background noise caused by the sea level flux of cosmic rays. The cosmic rays interact with detectors by including bursts of charge or light. These noise bursts can be conveniently grouped into two classes: the long distributed noise from the ionization wake of fast charged particles, and the creation of small intense bursts of charge by a nuclear reaction leading to a heavy recoiling nucleus. The analysis of this problem is illustrated by calculations of the rates at which bursts of electronic charge are created in silicon particle detectors by cosmic rays at sea level. We show how detector size and shape influence its background, and the influence of concrete shielding. An experimental spectrum is compared to the theoretical prediction to show the many contributions to the final detector background level.