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The mutual inductance between two coils is a key parameter in the inductively coupled wireless power transmission. The spiral rectangular coils are easier to implement than the circular ones, but the study of the mutual inductance of the spiral rectangular coils is not enough. In this paper, a new analytical calculation of the coaxial spiral rectangular coils is presented, which is simpler than the greenhouse method. The impact of the track thickness and width is also analyzed. The calculation results are verified by the existing methods and the experimental results. Based on these results, some guidelines for optimizing the coupling coefficient are given, when the received coil's size is limited by space constraints.