Motivic class computations provide a way of encoding certain algebro-geometric invariants in terms of elements of the Grothendieck ring of varieties or, more generally, of stacks.

We outline how to calculate the motivic classes of the stacks of semistable parabolic Higgs bundles and parabolic vector bundles with connections on a curve by employing a motivic version of a factorization formula used by Mellit to perform similar computations for the number of points over a finite field.

We conclude by briefly commenting on a potential generalization to the case of parabolic Higgs bundles and parabolic connections that have irregular singularities.

This is joint work with Roman Fedorov and Yan Soibelman.