What are the dimensions of a standard railway car?

There is no dimensional constant to "standardized" railway cars. Are you talking about the "Pullman-Standard"?

http://cs.trains.com/trn/f/111/t/127097.aspx

[Link added on August 21, 2016 by shuehorn]

Cargo: Liquid, solid or gas? Box car? Lumber car? Coal car? Intermodal? (single or double)

Passenger: Dining? Luggage? Sleeper? Commuter?

Too many to give a "standard".
http://www.alaskarails.org/fp/passenger.html

https://www.uprr.com/customers/ind-prod/attachments/ports/sail_alum.pdf

For models see below.
http://urbaneagle.com/data/RRstddims.html

[One link changed on August 21, 2016 by shuehorn]

Okay...how about AVERAGE? You know...the kind people buy for private use and then fix them up to suit themselves...and then hook 'em up behind an engine and away they go...toot toot!!!

Here is a 60 foot "double stacker".
http://upload.wikimedia.org/wikipedia/commons/e/e5/DTTX_724681_20050529_IL_Rochelle.jpg

New York's most common Train Car (Subway):

"The R44 was the first 75-foot (22.86 m) car for the New York City Subway. It was introduced for IND and BMT service because it was thought that a train of eight 75-foot cars would be more efficient than ten 60-foot (18.29 m) cars. Even with an overall increase in length, the R44's only had eight sets of doors per car (Ten 60-foot cars have 40 sets of doors whereas eight 75-foot cars only have 32 sets of doors)."
https://en.wikipedia.org/wiki/R44_%28New_York_City_Subway_car%29

Amtrak is, on average, 85 feet long.

You could try the UIC standards at
https://en.wikipedia.org/wiki/UIC_classification_of_railway_coaches

They have docs on Railway Loading Gauges, or take a trip to the Colorado Railway Museum at Golden.

Try this website on
http://www.aaprco.com

It deals with privately owned North American Railway Carriages.

[Link replaced on August 21, 2016 bu shuehorn]

The most common boxcars are 50'-6" to 60'-9" in length, 9'-4" to 9'-6" wide, and 10'-10" to 11' high. A hi-roof boxcar is 13' in height. These are inside dimensions. Corresponding exterior dimensions would be 55'-5" to 67'-11" in length, and 10'-6" to 10'-8" in width.

In the U.S., private rail cars are mostly owned by collectors who saved them from the scrap heap, restored them and now offer them for charter as a way to pay for their pricey hobby. The average cost to buy a restored car, or buy a junker and fix it up, can run to half a million dollars, says Bart Barton, president of the American Association of Private Railroad Car Owners. AAPRCO is the main membership organization for car owners and is a clearinghouse for information on private rail travel.

This site describes the various types of private railway cars, with illustrations, but I'm not finding any overall dimensions.
https://en.wikipedia.org/wiki/Private_railroad_car
Restored 1882 Pullman coach sleeper has these dimensions:
Length over end sills: 66'-7"
Width over side sills: 8'-5"