Stress triaxiality is a parameter that expresses the stress state and can be used as a variable to characterize the plasticity and fracture damage model of materials. It plays an important role in structural strength and failure analysis. The round bar tensile test with a notch can be used to calibrate the parameters in the plastic and damage models. However, there are two different formulas in the literature to calculate the triaxiality of the minimum cross-sectional axis of a notched round bar under tensile loading, which were proposed by internationally renowned scholars Bridgman and Wierzbicki, respectively. Their differences often cause confusion in application. Through refined finite element numerical analysis, this article attempts to clarify the validity and applicability of the two formulas. The results show that the Bridgman formula is more accurate only in the elastic stage and in a specific a/R range. The Bao-Wierzbicki formula, on the other hand, is in good agreement with the experimental data and simulation results, which can be used to calculate the arithmetic mean value of triaxiality during the entire tensile process. Based on further analysis, a new revised stress triaxiality formula in the plastic stage under elastic-perfectly-plastic condition is proposed, and the notch geometry effect and strain-hardening effect are further discussed. It is pointed out that notch ratio can affect the neck stress field. The smaller is the notch ratio, the closer is the stress triaxiality value in the elastic stage to 1/3. When the notch ratio is too small, it can also affect the change of stress triaxiality throughout the entire tensile process. The strain-hardening effect can change the trend of stress triaxiality during the stretching process, and an increase in the strengthening modulus will lead to a decrease in the peak value of the plastic stage. The higher is the strengthening modulus, the faster is the decrease of stress triaxiality after entering the plastic stage.