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Mutual inductance is a key parameter of the inductively coupled circuits such as transformers and contactless energy transfer systems. This parameter is particularly required to design the power electronics associated with each application. However, its value is usually extracted from measurements performed in a previously built prototype, which is an expensive and time-consuming task. In this paper, an analysis of the mutual inductance between two planar circular windings is developed. The analysis takes into account the effect of the media that can be part of the complete system. As a result, an analytical calculation of the mutual inductance with respect to the main parameters of the system such as the number of turns of the coils, geometry, frequency of the currents, and the properties of the media can be carried out. The analysis can also be used to explore the tendencies of the mutual inductance for design purposes and, thus, it allows speeding up the design process. The analysis has been verified by means of experimental results.