Not sure what you mean by estimate. Are you referring to cost to construct, design or size a culvert?

I suggest asking your community, county. etc. public works department for a rough cost by some unit that is convenient for them for street about as much traffic as you plan. If you happen to be one of them, next bet is a local road building contractor. Let them know you may want to negotiate a job sometime. Heavy traffic takes thicker pavement than a less used street. For any job like this you need plans and a detailed contract. That's where the CE comes in.

Sorry,
It is cost estimate to construct.
Thanks

The new street/road connects to existing road and will be about less than mile long. has drain in the middle so need pipe culvert for drainage

If you have a listing of Quantities you can use a source like RS Means for your area. The link below is another source for major construction activities. Hope these help.

http://www.get-a-quote.net/QuoteEngine/costbook.as...

Thank you

I guess that you are not working for a general contractor otherwise GC involved in this type of work can estimate such cost. Cost per miles not only depends on product cost but also on excavation including blasting if necessary and dewatering, refill, manpower, equipment usage, purchase of project plans, insurance, bidding, and possibly potential delays such as interruptions from OSHA, jurisdiction and insurance engineers and potential accidents.