Not very common, IMHO. You see an occasional relic that has had its barrel shortened in the field someplace, but you don't have guns coming out of factories with very short barrels.
What we think of as a " Carbine" today would be a rifle with a barrel between 14-20 inches long. Some would even argue with me that I am making such barrels too long! You don't see a lot of Rifled barrels much before the French and Indian War( 1756-1763- the "Seven Years War")in this country. The industrial age made the making of rifled barrels much easier, and with the same exacting tolerances as achieved with the boring machines made to use by hand power. 1840 is generally considered to be the " dawn" of the Industrial Age, but of course, there were steady developments in machinery and manufacturing techniques that made all that possible, going back many years- at least to the first decade of the 19th century.
The word Carbine really comes from either Spanish or Italian- 'Carbinieri" who were horse back police and soldiers. Wars didn't stop in Europe just because Napolean was defeated at Waterloo in 1814. For rather obvious reasons, horse mounted soldiers found it easier to load shorter barreled guns in the saddle, than longer barreled guns. Before they got shorter barrels, they were merely mounted troops, who got to the battle quickly by horse, then dismounted and fought from the ground like any ground pounder before and since. That same tactic was in use in the beginning years of our own Civil War.
As to what length barrel was used, there is a big difference in opinion, and some factual differences between the flintlock era, and the newer percussion era. The 1855 and 1842 vintage muskets had shorter barrels than found on the old Brown Bess smooth bores, but they would not be considered a "carbine" by today's standards. When you get to the first Breechloaders, then, you begin to see shorter barreled RIFLES show up, manufactured that way. I am thinking of the 1859 Sharps, and the Spencer cartridge guns that showed up between 1861 and 1865. By today's standards, those weren't Carbines, either, but the barrels were a lot shorter than the Springfield, and Enfield Rifles used by the Infantry on both sides of the Civil War.
There are a lot of short barreled rifles being made today that aren't "Replicas" of anything made in the past. :shocked2: :hmm: :thumbsup: :thumbsup: