It has long been realized that the thermal ratings of overhead transmission lines when computed deterministically, are typically conservative, resulting in underutilization of conductors. A probabilistic method to assess thermal capacity based on risk is presented in this paper. We address the potential impacts of thermal overload, the stochastic model of conductor temperature, and the quantitative risk which indicates the average "danger" of an overload. The continuous, short-time, and long-time thermal ratings are calculated using the risk of thermal overload. This method can provide technical justification for increased thermal capacity for a transmission line and an evaluation of risk for the given operating conditions. © 1998 IEEE.