The magnetic properties of ferromagnetic thin films down to the nanoscale are ruled by the exchange stiffness, anisotropies and the effects of magnetic fields. As surfaces break inversion symmetry, an additional effective chiral exchange is omnipresent in any magnetic nanostructure. These so-called Dzyaloshinskii-Moriya interactions (DMI) affect all inhomogeneous magnetic states either subtly or spectacularly. E.g., DMIs cause a chirality selection of the rotation sense and can fix the local rotation axis for the magnetization in domain walls (DW). But, they can stabilize also entirely different twisted magnetic structures. The chiral skyrmions a two-dimensional particle-like topological soliton is the ultimately smallest of these objects, which currently is targetted as a possible information carrier in novel spintronic devices. Observation and quantification of the chiral exchange effects provide for the salient point in understanding magnetic properties in ultrathin films and other nanostructures. An easy and reliable method to determine the DMI constant as materials parameter of asymmetric thin films is the crucial problem. Here, we put forth an experimental approach for the determination of the complete set of the micromagnetic parameters. Quasi-static Kerr microcopy observations of DW creep motion and equilibrium sizes of circular magnetic objects in combination with standard magnetometry are used to derive a consistent set of these materials parameters in polycrystalline ultrathin film systems, namely CrOx/Co/Pt stacks. The quantified micromagnetic model for these films identifies the circular magnetic objects, as seen by the optical microscopy, as ordinary bubble domains with homochiral walls. From micromagnetic calculations, the chiral skyrmions stabilized by the DMI in these films are shown to have diameters in the range 40-200nm, too small to be observed by optical microscopy.