We present a formal development of the tensorial rotational Hamiltonian using symbolic calculations. Algebraic manipulations thanks to the open-source Maxima software allow us to get formal expressions of use for various molecular spectroscopy problems. We first present some simple applications to the so-called semi-classical approach that allows the study of level structures in the molecular rotational energy spectrum. Then, we perform some comparisons between the tensorial approach and Watson’s Hamiltonian, giving exact effective molecular parameter correspondence formula between the two formalisms.