The development of nanoantennas is mostly done through time-consuming computer simulations. Nanoloop antennas, working in the terahertz, infrared and optical regimes, have used in a variety of applications, including as solar cells or optical sensors. In this paper we will present a theoretical analysis of thin-wire nanoloops, which leads to closed-form expressions to derive key antenna parameters: radiated electric fields, radiated power, radiation resistance, directivity and gain. Results for gold thin-wire nanoloops are validated with full-wave simulations, and the presentation includes a comparison with classical nanodimensional PEC loops, emphasizing the differences and similarities from a physical point of view. While full-wave simulations can take on the order of hours, the analytical expressions can be evaluated on the order of seconds, thus allowing a wider assessment of the usefulness of these nanoantennas in practical applications.