Various engineering techniques are used for optimal gas-dynamic design of centrifugal compressors. This includes a universal modelling method that consists of software programs developed at Peter the Great St. Petersburg Polytechnic University. Tangential exit nozzles are elements of the centrifugal compressor flow path. The analysis of the results of the tangential exit nozzle calculations using the current mathematical model showed a need of improvement. The following main provisions formed a basis for a new model: the size of the passage is determined using the flow rate equation at the entrance and exit of the output unit (the calculated cross sections should be increased by 25–35% according to the recognized recommendations by Russian experts); the real nature of the flow in the output unit is taken into account by introducing an empirical coefficient in the equation of the circumferential component of velocity; the output diffuser is designed taking into account the optimal angle of expansion of an equivalent conical diffuser; the scroll tongue is shifted from a section with an angle of expansion of 0° to a section with an angle of expansion of 30°, which aids levelling the circumferential flow parameters and reduces total losses. To simplify the calculation process, a constant density along the scroll length is adopted in the mathematical model. The circumferential component of velocity is also determined approximately using the flow continuity equation without taking viscosity into account. Losses in scrolls and annular chambers are calculated in the radial and meridional planes. In the radial plane, the main losses are friction losses, whereas in the meridional plane, the main losses are due to expansion. For a trapezoid scroll, these pressure losses are determined depending on the scroll’s expansion angle. In the off-design operating modes, incidental losses due to impact flow around the scroll tongue are added. The presented model was implemented in the new version of the universal modeling method. The mathematical model was identified by the results of the commissioning test of the turboexpanders and turbochargers.