It is the big problem to evaluate the fatigue limit σw in order to safely design structures and machines. Under the condition of the fatigue crack initiation limit σw1, the present author defined the initial crack size √area using the characteristic elastic field of the notch, the half length of the fatigue crack a and a notch depth t. Using this √area, the methods of calculating ΔKth and σw1 were proposed. In addition to it, in this condition it is made sure that ΔKth exists on the band from ΔK th prediction line of the micro fatigue crack within 18% error. Using ΔKth calculated by the prediction line and the value of Vi, this evaluating method of σw1 was confirmed with annealed 0.35% carbon steel. As a result, it was confirmed that this method to evaluate σw1 is within 18% error. Moreover it was also confirmed that the σw1 value by this prediction method is within 10% error when the predicted σw1 value is greater than σw2.