Inhaled radioactive is a unique hazard. Once inhaled the radioactive material is translocated within the body via incorporation into the metabolism and immune response. While metabolizing, the radioactive material is irradiating nearby tissue. Since the distribution of radioactive material changes over time, biokinetic modelling tracks the movement of the radioactive material within organs and tissues. To determine the impact of the input parameters into biokinetic modelling, a software called REDCAL (Radiation Exposure Dose Calculator) was developed in Python to handle statistically sampled parameters to compute the radiation dose from radionuclides of concern for emergency response planners. REDCAL handles the inhalation of radioactive particles and subsequent deposition within the airways. Following the deposition computations, REDCAL tracks the movement of radioactive material within the body and computes the effective dose to the individual over a lifetime. With statistically sampled input parameters, REDCAL was used to generate 3,410,000 effective dose coefficients to analyze the influence of the input parameters on the resulting dose. As sets of dose coefficients were made for each radionuclide and its associated lung clearance type(s), a defined distribution of its effective dose coefficient as a function of inhaled particle size, in AMAD, were generated to inform the sampling needing for computing derived response levels (DRLs) by in Turbo FRMAC by the Federal Radiological Monitoring and Assessment Center (FRMAC). This dissertation covers the methods, mathematics, and concepts required to compute particle deposition in the airways, solve biokinetic models, and compute effective dose from radiation sources with time-dependent concentrations.