Conducting loops have been rigorously analyzed in the microwave/RF regime due to their simplicity and versatility. In the terahertz, infrared and optical regimes nanoloops are extremely promising for a variety of applications, including as solar cells or optical sensors. However, due to the complex behavior of metals, a complete theoretical derivation of the radiation parameters of a nanoloop at these frequencies has not yet been performed. This paper will extend the formulation of thin-wire Perfect-Electric Conductor (PEC) loops to include the effects of loss and dispersion. Closed form expressions for the radiated fields, directivity and gain will be presented. The expressions involve integrals of Bessel and Lommel-Weber functions as well as Q-type integrals. Various series representations for these integrals will be presented along with guidelines on which are the most efficient. Validation of the equations will be provided through a comparison with full-wave solvers. While these simulations take on the order of hours, the analytical expressions can be evaluated on the order of seconds.