This depends a lot on the position and cannot be answered generally. If you have a forced line, i.e. a position where there are only few candidate moves at every step, a grandmaster can calculate many moves. I am reluctant to give a concrete number because it really depends, but to give you a rough idea, let's say 20 moves.
On the other hand if the position is rather closed, of the maneuvering type, with many equal alternatives at every step, the calculation depth will be much smaller, simply because the number of variations will be much much larger in this case. And even if you calculated 20 moves deep you might not come to a conclusion on which line is best, because 20 moves in the future the position might still be equal. In this case a grandmaster would typically only calculate a couple of moves deep (if at all) in order to check that he is not blundering anything to a tactic.
As you can see from this description, pure calculation strength is only needed sometimes in a game and certainly not the only reason that grandmasters are much better than the rest. Unlike computers, humans do not play chess by calculating many moves in advance. The strength of human players over computers is that they can evaluate the position and develop a plan based on the evaluation. Humans focus more on recognizing patterns and play moves based on these patterns.
So, grandmasters are grandmasters, because they are good at all parts of the game:
- calculating many moves ahead
- evaluating a position correctly
- finding the right plan
- good at defense: using tactical ideas, standard methods, pure calculation...)
- good at openings: knowing main lines, side lines, recognizing wrong moves in an opening and knowing how to react to them, knowing the ideas behind openings...
- good at endgames: as with openings, there is a huge body of theory that you can study; also some grandmasters like Carlsen, are said to be particularly good at endgames beyond the known theory
- pattern recognition abilities: to recognize tactics and other known motives
- personal traits, physical fitness