Nowadays, most studies of the dynamic characteristics of annular gaps focus only on the force characteristics due to translational motions, while the tilt and moment coefficients are less well studied. To expand the knowledge of the additional coefficients, we investigate both the dynamic force and the dynamic and moment characteristics of annular gaps. First, the rotordynamic influence of annular gaps is recapitulated. Second, a new simulation method is presented, using a perturbed integro-differential approach in combination with a Hirs’ model and power law ansatz functions for the velocity profiles to calculate the dynamic force and moment characteristics. Subsequently, an extensive parameter study is carried out. To evaluate whether the hydraulic tilt and moment coefficients need to be considered, an effective stiffness is defined and the influence of the annulus length, an eccentrically operated shaft, the center of rotation, a modified Reynolds number, the flow number, and the pre-swirl is investigated. It is shown that despite the annulus length, the flow number as well a modified Reynolds number are crucial for the relevance of the additional coefficients. This leads to a simple three-dimensional diagram, which makes it possible to assess the necessity of including the additional coefficients on the basis of the three variables.