A simple model for estimating the hysteresis energy loss of coated conductors under a general load line was studied. We took advantage of the characteristic line I(b)(H(a)) to determine the major parameters used in this model. The value of I(b)(H(a)) was based on the scanning Hall probe measurements (SHP) on a Sm(1)Ba(2)Cu(3)O(7-delta) coated conductor. During SHP measurement, a magnetic field ( Ha) and current (I(a)) were applied simultaneously and were varied along 11 different load lines. From the values of SHP measurements, the current density profiles, J (x, H(a), I(a)), were calculated using a numerical inversion method. We define the quantity Ib = integral(w)(-w) vertical bar J (x, H(a), I(a)) vertical bar dx and we calculated I(b) at many points (H(a), I(a)) in every load line. We found that when I(a) is less than I(b) and the flux trap regions are absent, the values of I(b) for all points (H(a), I(a)) constitute a single line I(b)(H(a)), which can be easily extrapolated to a high field. This line provided a major parameter for our model.