Current load capacity isn't a matter of copper area rather than trace cross section (width multiply thickness). You can easily calculate trace resistances and related resistive power dissipation.
For 160 A, I would think about at least 4 to 6 ounces copper weight (140 to 210 um thickness) or similar multilayer sandwich design. Design rules for thick copper PCB are rather restricted (minimal structure width, spacing), but it can be done.
A rule of thumb for a quick estimation. Sheet resistance of 1 oz. (35 um) copper is about 0.5 mOhm. That means a 100 mm long trace of 10 mm width has e.g. a resistance of 5 mOhm (sheet resistance * length / width). Scale with copper weight/1 oz.