Mass of a black hole I know that if a star collapses into a volume with radius less or equal to the Schwarzschild radius $r_s=\frac{2GM}{c^2}$ then a black hole is created and it has the same mass of the star that gave it origin. But is there a way to calculate the mass of a black hole without knowing the volume of the star?
 A: 
[a black hole] has the same mass of the star that gave it origin

No, not really. A stellar-mass black hole is formed after a star with mass around 20 times that of our sun collapses due to lack of core fusion and by some (as of yet) unknown process, rebounds and explodes. This explosion, a Type II supernova, kicks off something like 90% of its matter. Thus, the black hole would be something around the 5 solar mass range.

is there a way to calculate the mass of a black hole 

Well you can't actually observe black holes in free space (because you can't see them), you need to infer it by using something around it (either a star or gas cloud) and computing the mass from Kepler's laws.
A: |[a black hole] has the same mass of the star that gave it origin
as Kyle figured out, the mass of the black hole correlates with the star, but in general a star loses much mass in a supernova.
Furthermore, there are many more ways to create a black hole, like colloding neutron stars in theory, even at the LHC/Cern, colliding nuclei could lead to black holes. So they can be large, or very small.
To calculate the mass of a black hole: well, that's a bit tricky, because you can fully describe a black hole by the parameters: 1) mass, 2) electric charge, 3) rotation momentum.
So the question is: how to calculate the mass from what?
What you could do: measure the Schwarzschild radius or mesaure the gravity field of the black hole to derive it's mass. But there is no real way to "calculate" the mass of a black hole. Its like if you want to calculate the amount of water in a bucket. It just depends on the amount of water in the bucket.
About your comment on GR: At the current stage of phsics, the general relativity theory is the only theory, that can describe black holes. They only exist in this theory.
