Carnival does not have a "formal" night anymore... it is called "Cruise Elegant" and is a bit more casual than the former "formal" night.
Below is directly from Carnival's website:
Cruise Elegant Dining Dress Code: Gentlemen - Dress slacks, dress shirts. We also suggest a sport coat. If you wish to wear suits and ties or tuxedos, by all means we invite you to do so. Ladies - Cocktail dresses, pantsuits, elegant skirts and blouses; if you‘d like to show off your evening gowns, that's great too!
Not permitted in the dining room during the Cruise Elegant dinner for ladies and gentlemen: shorts, gym shorts, T-shirts, beach flip-flops, bathing suit attire, jeans, cut-off jeans, sleeveless shirts for men, sportswear, and baseball hats.
Notice that a tie is not required....