We calculated the co-seismic Earth rotation changes for several typical great earthquakes since 1960 based on Dahlen¡¦s analytical expression of Earth inertia moment change, the excitation functions of polar motion and, variation in the length of a day (ΔLOD). Then, we derived a mathematical relation between polar motion and earthquake parameters, to prove that the amplitude of polar motion is independent of longitude. Because the analytical expression of Dahlen¡¦s theory is useful to theoretically estimate rotation changes by earthquakes having different seismic parameters, we show results for polar motion and ΔLOD for various types of earthquakes in a comprehensive manner. The modeled results show that the seismic effect on the Earth¡¦s rotation decreases gradually with increased latitude if other parameters are unchanged. The Earth¡¦s rotational change is symmetrical for a 45° dip angle and the maximum changes appear at the equator and poles. Earthquakes at a medium dip angle and low latitudes produce large rotation changes. As an example, we calculate the polar motion and ΔLOD caused by the 2011 Tohoku-Oki Earthquake using two different fault models. Results show that a fine slip fault model is useful to compute co-seismic Earth rotation change. The obtained results indicate Dahlen¡¦s method gives good approximations for computation of co-seismic rotation changes, but there are some differences if one considers detailed fault slip distributions. Finally we analyze and discuss the co-seismic Earth rotation change signal using GRACE data, showing that such a signal is hard to be detected at present, but it might be detected under some conditions. Numerical results of this study will serve as a good indicator to check if satellite observations such as GRACE can detect a seismic rotation change when a great earthquake occur.