Laser welding is an essential technology for many applications. However, due tothe complex non-linear interactions between parameters and the emergence ofweld defects, there are still many challenges in predicting the physical transfor-mations occuring during welding. For these predictions, Suder suggested reducingthe number of parameters by using higher-level parameters such as power den-sity, interaction time, and specific point energy. He predicts that, for a givenpower density, the weld penetration depth is logarithmically correlated with thespecific point energy. In this study, we experimentally investigate the extensionof this law by testing different diameters of the fiber used to deliver the laserbeam. We demonstrate that this log law also depends on the beam size and pro-file. Our research establishes a generalised linear relationship between the areaof the cross-section of the weld and the specific point energy.