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The complexity in the evaluation of the radiation quality factor Q of small antenna lies in the calculation of the stored energy. Previous authors proposed several analytical expressions for simple antennas to obtain the Q which is of practical importance because of its relationship to the antenna bandwidth. This paper presents a simple method to calculate the Q using FDTD giving us accurate results. Examples of a linear dipole antenna and an inverted L antenna along with their results are presented to show the validity of the lower bound presented here