<p>Centrifugal compressors encounter unavoidable uncertainties during their operation. This paper presents and discusses a comprehensive uncertainty quantification analysis that affect the flow characteristics and performance parameters of the NASA low-speed centrifugal compressor. These stochastic conditions include inlet total pressure, inlet total temperature, mass flow rate, inlet flow angle, and rotational speed, with Beta probability distribution. To quantify these effects, the polynomial chaos method is employed. Additionally, a sensitivity analysis using Sobol indices is performed to determine the impact of each random input parameter. This research finds that the isentropic efficiency and flow field are significantly influenced by random operational conditions. Uncertainties, especially in rotational speed and inlet flow angle, play a crucial role in affecting Mach number around the blade, the static pressure coefficient, and the entropy production rate. Minor fluctuations of 0.3% in mass flow rate, 0.07% in inlet total pressure, and 1% in rotational speed result in changes of 10.48% and 1.52% in normalized input power and isentropic efficiency, respectively. The present study offers thorough insights into the influence of uncertain working conditions on centrifugal compressor efficiency and provides guidance for the future development of more robust centrifugal compressor designs.</p>