Like the title says, is there a standard somewhere?
I got a kick out of that question. DIN is short for Deutsche Industrie Norm (a standard for German industry). The standard is actually DIN 7736. The exact dimmensions are 178mm x 50mm x 150mm. (one inch is 25.4mm).
The DIN standard actually posts a depth. That was news to me. So I guess in order for an auto manufacturer to say that they have a DIN compatible radio they need to have at least 150mm depth.