Transverse gradient undulator (TGU) is attracting more and more attentions, especially for the rapid progress of laser plasma accelerator techniques. The transverse gradient of TGU is usually given by an empirical formula simply derived from the empirical formula of a uniform-parameter undulator. In this paper, we numerically investigate the transverse magnetic field of TGUs using the RADIA code. Through many simulations for TGUs with different magnet structures, we have given the dependences

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... transverse gradient parameter on the cant angle, the undulator period and the average gap. Based on these results, when the cant angle is small and the rate of the gap and period is in the range of 0.4-0.6, the simulation results agree with the empirical formula well. But, with the growing of the cant angle, or with the growing of the deviation of the rate of the gap and period from the range of 0.4-0.6, the difference between the simulation results and the empirical formula becomes larger.