In this paper, formulas are developed for the calculation of the effective thread friction radius in fasteners, in order to determine the thread friction torque component. Due to the lack of exact formulas in the literature, current practice uses the average value of the minor and major thread radii, as an approximation, for determining the thread friction torque component. Results provided by these formulas are compared with those given by the current practice that uses the average value of the minor and major thread radii, instead of the exact value. It is well known that the torque-tension relationship in threaded fastener applications is highly sensitive to the friction torque components: between threads, and under the turning fastener head or nut. Even moderate variations or inaccuracies in determining the friction torque components would significantly impact the fastener tension and the joint clamp load. High accuracy in the estimation of the friction torque components is critical, as it directly affects the reliability, safety, and the quality of bolted assemblies. This analysis focuses on the thread friction torque component. The new formulas for the thread friction radius are developed for a mathematical model of a bolted joint using five assumed scenarios of the contact pressure between male and female threads. Because of the fact that the variation in the sliding speed of various points on a thread surface is insignificant, a uniform thread friction coefficient is used in the analysis. However, a contact area weighted average value is used for the thread friction coefficient. Numerical results and error analysis are presented in terms of a single nondimensional variable, namely, the ratio between the major and minor thread radii.