Measurement precision is often required in the process of material parameter extraction. This fact is applicable to terahertz time-domain spectroscopy (THz-TDS), which is able to determine the optical/dielectric constants of material in the T-ray regime. Essentially, an ultrafast-pulsed THz-TDS system is composed of several mechanical, optical, and electronic parts, each of which is limited in precision. In operation, the uncertainties of these parts, along with the uncertainties introduced during the parameter extraction process, contribute to the overall uncertainty appearing at the output, i.e. the uncertainty in the extracted optical constants. This paper analyzes the sources of uncertainty and models error propagation through the process.