A simple model for estimating the hysteresis energy loss of coated conductorsunder a general load line was studied. We took advantage of the characteristic lineIb(Ha) to determine the major parameters used in this model. The value ofIb(Ha) was based on the scanning Hall probe measurements (SHP) on aSm1Ba2Cu3O7 − δ coated conductor. During SHP measurement, a magnetic field (Ha) andcurrent (Ia) were applied simultaneously and were varied along 11 different loadlines. From the values of SHP measurements, the current density profiles,J(x, Ha, Ia), were calculated using a numerical inversion method. We define the quantityIb = ∫ − ww|J(x, Ha, Ia)| dx and we calculatedIb at many points(Ha, Ia) in every load line. Wefound that when Ia is less than Ib and the flux trap regions are absent, the values ofIb for all points(Ha, Ia) constitute asingle line Ib(Ha), which can be easily extrapolated to a high field. This line provided a major parameter forour model.