This is what professional engineers get paid to determine. It depends on the level of protection required (can flow overtop the road? If so how often?), the drainage area contributing to the culvert, the rainfall patterns of the area, the channel charecteristics of the downstream channel. After all this is determined, you can size the culvert and then, does it fit under the road? Will you have to raise the road to get the culvert under it? What kind of bedding is required? There really is no rule of thumb that I'm aware of for quick sizing the culvert. You can probably hire an engineer to design it for you (shouldn't cost too teribly much) and then you have the protection of his errors and omisions insurance in case something does go wrong.
Brian