Welded joints are prone to fatigue cracking with the existence of welding defects and bending stress. Fracture mechanics is a useful approach in which the fatigue life of the welded joint can be predicted. The key challenge of such predictions using fracture mechanics is how to accurately calculate the stress intensity factor (SIF). An empirical formula for calculating the SIF of welded joints under bending stress was developed by Baik, Yamada and Ishikawa based on the hybrid method. However, when calculating the SIF of a semi-elliptical crack, this study found that the accuracy of the Baik-Yamada formula was poor when comparing the benchmark results, experimental data and numerical results. The reasons for the reduced accuracy of the Baik-Yamada formula were identified and discussed in this paper. Furthermore, a new correction factor was developed and added to the Baik-Yamada formula by using theoretical analysis and numerical regression. Finally, the predictions using the modified Baik-Yamada formula were compared with the benchmark results, experimental data and numerical results. It was found that the accuracy of the modified Baik-Yamada formula was greatly improved. Therefore, it is proposed that this modified formula is used to conveniently and accurately calculate the SIF of semi-elliptical cracks in welded joints under bending stress.