It is known that inserting the position vector \({x}\) into the divergence theorem yields simple expression for the volume integral, and leads to the possibility to evaluate the expression by integration over the surface. This can be applied for providing the volume or the center of a volume as well, which is identical to the entire mass or the center of mass for constant density of a material body. It is shown that the entire idea can be extended to the calculation of the mass moment of inertia tensor. As a side product, the area moment of inertia tensor is discussed as well. All expressions are developed in a coordinate-free representation. Using, for example, triangulation techniques, simplified approaches can be derived for nearly arbitrary volumes and areas. Thus, the numerical treatment on the basis of triangulation is provided as well. Examples and coding will demonstrate the outcome of the results indicating a simple implementation. However, an inherent consequence of the discretization is the emergence of non-symmetric inertia tensors. This issue is discussed as well.
