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This paper presents a closed expression of the layered-plate factor used to calculate the coil eddy-current impedance over the multi-layer plate conductor.By using this expression,the general series of eddy-current impedance can be written directly without solving the undetermined constant equations.The series expression is easy to use for theoretical analysis and programming.Experimental results show that calculated values and measured values are in agreement.As an application,when the bottom layer of the layered plate is a non-ferromagnetic thin layer conductor and the product of the thickness and conductivity of the layer remains unchanged,using the layered-plate factor expression proposed in this paper,it can be theoretically predicted that the eddy-current impedance curves corresponding to different thin layer thickness values will coincide.