It is necessary to develop a technique that can be used to estimate cracks, which indicates a typical type of damage, using sensors to achieve the structural safety of circular steel-tube structural members widely used in infrastructures. Impedance techniques have been actively investigated to detect local damage, such as cracks. The cracks were estimated by experimentally investigating the relationship between the cracks and impedance signals using a damage index. The aim of this study is to investigate the correlation between the change in impedance signal and the change in the analytically obtained equivalent bending stiffness of cracked beams owing to crack formation and propagation in a circular steel-tube beam. In other words, the impedance signal was measured while gradually inducing cracking in circular steel-tube cantilever beams, two damage indices were obtained, and the results were compared with the analytically obtained equivalent bending stiffness of cracked beams constructed using an energy method. It was found that a close correlation between both the damage index for the impedance signal and equivalent bending stiffness for the crack location and the size of each damage case existed. Based on this correlation, the structural characteristics of the current state of a structure can be evaluated more accurately using the damage estimation results, and the behavior of the structure can be predicted using the analysis model.