Never bothered to measure, but I definitely leave plenty of space in the bottle when I force-carb. 1.5 - 2" below the neck, I'd guess. If you don't you'll loose most of the CO2 cartridge out the vent.
I also only replace empty cartridges one at a time. In other words, I'll tap a flat, chilled bottle and load just one CO2 cartridge (other side has an empty in it). Wait 24 hours, then load one more cartridge. After 48 hours, it's ready to drink.