Abstract: To address the problems that the physical mechanism of the stage-discharge relationship is not clear and the uncertainty sources of estimated discharge is not adequately considered, current study used the Shijiao hydrological station of the North River basin as an example to derive the stage-discharge relationship. Based on the BaRatin model, current study evaluated the discharge measurement error and the effect of the calibration sample selection on the uncertainty of the estimated discharge. It was found that the stage-discharge relationship for the wide and shallow rectangular section of the river channel is a power function, where its coefficient can be expressed by roughness, river width, and energy slop, and the index is a constant value of 5/3. The total uncertainty of the estimated discharge decreases by 32% when considering the discharge measurement error. Doubling (Tripling) the samples drops the total uncertainty of the estimated discharge by 12% (34%). The conclusions of this study are:① The method of establishing the stage-discharge relationship here can be extended to different types of hydrological stations; ② The high water measurement error has significant impact on the calibration accuracy, and it is recommended to improve the high water flow measurement accuracy; ③ Information redundancy exists in the measured data, particularly in the low water measurements. The proposed method requires less calibration data, which can reduce the cost of discharge compilation.