It says about 2.7 million Americans are currently in the military.
I did specify "hotly engaged in war"...
Plus, I think there are closer to 15-30+ billion people in each memberworld, not 5 billion.
Might be. Vulcan in STXI had six billion, despite not being particularly fertile. When Earth was Borgified in ST:FC, Data expressed surprise at it having a population of 9 billion - but we don't know if that was exceptionally low or exceptionally high. Also, most of the colonies we have seen have been tiny affairs, with populations numbering in the thousands rather than millions - yet in TAS "One of Our Planets is Missing", the very outermost of UFP colonies was said to have a population of "millions", possibly suggesting that colonies closer to the UFP core could be relatively heavily populated after all.
Anyone know what percent of people were in the military during the age of sail, when navies did more exploring?
The thing is, people really weren't "in the military" much those days. The navies would hire some full-time professionals to sail the ships, but most of the soldiers would be drafted as needed. In theory, 50% of the nation's population could be drafted in extreme crisis, while the other 50% would be engaged in the war effort in some way or another, too. And in practice, the major sailing nations of the era were engaged in war most of the time back then.
Let's have, say, the War of the Spanish Succession in the beginning of the 18th century - an Europe-rattling conflict with overseas intrigue, one where the nations couldn't afford to hold back. France committed some 225,000 men at the height of the crisis, and had a population of 21 million, being a true kingpin nation in Europe. The population of Spain at the time is a matter of some controversy, so their initial commitment of 20,000 troops might account for 0.4% (out of 5 million) or more like 0.2% (out of 10 million). When the war moved deep onto their turf, the number was increased about fivefold. But that'd be at the height of the crisis; and even there, at any given time, there'd be fewer men at arms, and of course there would have to be major lulls in fighting because the manpower was needed for harvesting as well. Only a tiny fraction of the forces would be professional soldiers - perhaps one per mil of the troops would commit themselves totally to the war.
England fought from an overseas position, so her contribution would have a greater percentage of professional fighters who would be expected to remain on a war footing all year around. The island supported about 5 million people at the time, and sent some 40,000 men in all. That was a back-breaking commitment, but proved worth the while, and is probably our best analogy to what the UFP might commit to an interstellar war that wasn't about ultimate survival.
Timo Saloniemi