Abstract Fatigue life prediction for machine components is a key factor in the industrial world and several methods can be traced in technical literature to estimate life of notched components. The paper correlates the classical stress-gradient approach, here after called support factor (SF) method, proposed by Siebel, Neuber and Petersen with the modern theory of critical distance (TCD) approach by Tanaka and Taylor. On the one hand, the main asset of the SF method is that it relies only on the knowledge of the maximum stress and stress gradient in the hot spot. By contrast, the TCD needs the calculation of the stress distribution for a finite depth inside the material. On the other hand, the main drawback of the SF method is that the material parameter ρ* is available only for a limited collection of materials and moreover the experimental procedure to retrieve this parameter is not clearly defined in the technical literature. In order to overcome this limitation, the paper investigates the correlation between the material parameter ρ* and the critical distance L of the TCD by relying on a specific stress function. A comparison between the SF method and the TCD is then performed by considering three different benchmark geometries: a general V-notch in a plate, a pressure vessel and an industrial oleo-hydraulic distributor. Effective stresses are analytically retrieved and compared using both methods for the first two benchmarks and with the help of an elastic finite element analysis for the last one. The resus appear good in terms of fatigue life prediction, especially for the industrial case study.