Surface cracks in butt-welded joints usually occur in places with increased stress concentrations. The stress concentration factor (SCF) can be calculated using an empirical equation, with five geometric parameters of a butt-welded joint (thickness of the base material, toe radius, weld toe angle, weld width, and reinforcement height). However, in anindustrial environment, it is impractical and sometimes even impossible to measure all five geometric parameters with sufficient accuracy. In this study, eight experiments on butt-welded joints were performed. All samples were scanned with a 3D scanner, and the geometric sizes of the welded joints were measured using computer software. A modified empirical expression proposed by Ushirokawa and Nakayama was used to calculate the SCF; the expression was adjusted in such a way that the SCF was calculated by knowing only the toe radius. In addition, four new expressions were proposed for the calculation of the SCF by knowing the toe radius in relation to the weld toe angle; the expressions were then compared and analysed. Additionally, the values of the stress concentrations in the butt-welded joints were obtained using afinite element method (FEM). The SCFs calculated using the four methods were compared and further discussed. Our data suggested a new accurate and straightforward approach for calculating the SCF by knowing only the weld toe radius.