It varies a little with each airline i flew earlier today on American with a box I made out of two of the smaller fedex 'art boxes' (they are roughly 25x35 id say) . The airline had an inches limit and weight limit (had to be under 100 lbs - i forgot the inch limit but my box is about 3.5 feet by 4.5 feet , 5 inches wide .) It was supposed to cost me 200 bux to check it as 'oversize' but I printed out my luggage tags at a kiosk normal and the check in girl was cool and didn't want to bother with changing it to oversize, so no fee.
Carry-on I brought a thick poster tube that was 4 feet long / 5 inches wide - It fit diagnally in overhead on my first plane and the second plane was older with smaller compartments so they just temp-checked it and I got it from them right when I got off the plane. If you get a tube make sure it's thick because people were definitely trying to jam their luggage into it because it looks like an empty space. First class appeared to have much longer compartments that would be an easier fit. Id just prepare the tube as if it might need to get checked and have some money ready for an extra bag fee if you're flying coach , just as a precaution.