I dont think that has calculated yet . Its evident from experiment that the proton mass is approx 1 GeV and is very difficult to calculate that from quarks and gluons because of "complex" strong interactions between them...

Yes, it is not trivial to calculate the nucleon mass from first principles but it has been done within a so called "lattice gauge theory" using supercomputers. More in:

http://physicsworld.com/cws/article/news/2008/nov/21/proton-and-neutron-masses-calculated-from-first-principles

Hey nice article Adam, I'll dig more on the group that did the work. Thanks

BTW, my header has a typo, not 983 MeV , should be 938 MeV.