I have never even heard of a metric angular unit. Well, the radian measurement of a plane angle can be defined as a ratio of the length of a circular arc divi

I have never even heard of a metric angular unit. Well, the radian measurement of a plane angle can be defined as a ratio of the length of a circular arc divided by the length of the arc's radius, so the "metre per metre" (a.k.a. "1") is a legitimate (derived) metric angular unit.