Despite the accuracy and non-intrusive nature of Electrochemical Impedance Spectroscopy, the impedance spectra of commercial Lithium-ion cells are notoriously hard to interpret. Consequently, the literature is filled with various equivalent circuit models, which differ greatly in their physical significance, but which produce very similar impedance spectra. In this paper, explicit formulas are given to convert between various equivalent circuits made of resistors and capacitors of the sort discussed in the literature. Furthermore, all these formulas have been implemented in a Python program, in the hope that studies done assuming one circuit might be compared to studies done with a different circuit, for instance. This paper considers cases where two different circuits can produce two impedance spectra which are identical. For instance, explicit conversions are given between Ladder circuits, Voight circuits, and Maxwell circuits for various time constants. This gives a conceptual foundation to explore the more difficult case of circuits producing impedance spectra which are similar to each other (e.g. within 5%). (c) The Author(s) 2018. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 License.