The relationship between the area and the depth of the storm precipitation is a important subject with regard to the weather forecast, the flood control and the hydrology. In the past, there was only experience curve for precipitation area and depth but no theoretical relation. In this paper, the theoretical relationship between the area and the depth is deduced by the principle of the maximum entropy. The theoretical relationship has been verified by analyzing about 90 storms happening in China and the United States.The result shows that the above mentioned area-depth formula of the precipitation is in keeping with the truth.