Do airlines use a software to calculate center of gravity?
Most airlines of any size use software to calculate the c.g., either their own software or vendor software.

Passenger aircraft weight &amp; balance is relatively trivial compared to cargo aircraft w&amp;b, where such things as floor loading, lateral imbalance, and monocoque limits can come into play.

http://www.champ.aero/ is one provider of that service and software for cargo aircraft for those companies not wishing to program their own.

Fuel efficiency is one advantage of loading to given c.g. An oft-used method is to load to a specified zero fuel weight c.g. For example, on 747 aircraft through the -400 models, a zfw c.g. of 26.6% mac is a typical target.

If you want to see and play with a free, online, open-source w&amp;b system for cargo aircraft, go to http://terryliittschwager.com/WB/index.php.