The Dzyaloshinskii–Moriya interaction (DMI) in magnetic objects is of enormous interest, because it generates built-in chirality of magnetic domain walls (DWs) and topologically protected skyrmions, leading to efficient motion driven by spin–orbit torques. Because of its importance for both potential applications and fundamental research, many experimental efforts have been devoted to DMI investigation. However, current experimental probing techniques cover only limited ranges of the DMI strength and have specific sample requirements. Thus, there are no versatile methods to quantify DMI over a wide range of values. Here, we present such an experimental scheme, which is based on the angular dependence of asymmetric DW motion. This method can be used to determine values of DMI much larger than the maximum strength of the external magnetic field strength, which demonstrates that various DMI strengths can be quantified with a single measurement setup. This scheme may thus prove essential to DMI-related emerging fields in nanotechnology.