How is the "Soldiers" demographic in Civ 5 calculated?

Solution 1:

The formula is rather simple: 2000*n^0.5

Now, it is not so very obvious (or known) how n is calculated, however this seems to be the basic formula (it somewhat matches the curve with only a few slight deviations): (1.15 * combat strength) ^ 1.5

Mind you, this does take into account damaged units.

There are additional percent modifiers for some subset of innate promotions, which weren't figured out exactly. for example the Jaguar and Mohawk warrior both start at 25% higher than their counterparts, an anti tank gun starts at 25% above it's base 222 (277), while an anti aircraft gun starts at 95% above (432).

Now, there is a more accurate formula which I however didn't test yet myself, for reasons of complexity. Anyway, here you go:

You have to click it to properly read it, I couldn't really have made it any bigger due to how long it is.

Source