Estimating the health effects of radon exposure is of great interest because radon is considered the second leading cause of lung cancer after smoking. The dose-response curve is not well understood at low-dose levels where radon exposure is estimated. Therefore, the health mechanisms of radiation due to radon progeny at the cellular and molecular levels are of interest for providing an indication of a possible threshold value above which the exposure may indicate cancer formation. In this paper we present a macroscopic and cellular level numerical analysis of the radon-induced dose estimates based on the Geant4 code system. Macroscopic estimates are assessed based on patient-specific computer tomography scans that provide geometries easily applicable to modeling radiation effects of the radon progeny sources. A small tissue volumes analysis based on the Geant4 code system is developed so as to provide information about the interactions and particle track structures at the microscopic (cellular) levels producing the dosimetric effects of radon short-lived progenies. The results presented in this paper also call attention to the capabilities of Geant4 to provide radon-related dosimetric parameters of large and small-scale biological systems.