Abstract: We characterize superconducting antenna-coupled hot-electron bolometers for direct detection of terahertz radiation operating at a temperature of 9.0 K. The estimated value of responsivity obtained from lumped-element theory is strongly different from the measured one. A numerical calculation of the detector responsivity is developed, using the Euler method, applied to the system of heat balance equations written in recurrent form. This distributed element model takes into account the effect of nonuniform heating of the detector along its length and provides results that are in better agreement with the experiment. At a signal frequency of 2.5 THz, the measured value of the optical detector noise equivalent power is 2.0 × 10-13 W · Hz-0.5. The value of the bolometer time constant is 35 ps. The corresponding energy resolution is about 3 aJ. This detector has a sensitivity similar to that of the state-of-the-art sub-millimeter detectors operating at accessible cryogenic temperatures, but with a response time several orders of magnitude shorter.