The direct current potential drop (DCPD) method and the unloading compliance (UC) method with a crack opening displacement gauge were applied simultaneously to the Zr-2.5Nb curved compact tension (CCT) specimens to determine which of the two methods can precisely determine the crack initiation point and hence the crack length for evaluation of their fracture toughness. The DCPD method detected the crack initiation at a smaller load-line displacement compared to the UC method. As a verification, a direct observation of the fracture surfaces on the curved compact tension specimens was made on the CCT specimens experiencing either 0.8 to 1.0 mm load line displacement or various loads from $50\%;to;80\%$ of the maximum peak load, or $P_{max}$. The DCPD method is concluded to be more precise in determining the crack initiation and fracture toughness, J in Zr-2.5Nb CCT specimens than the UC method.