How is weak isospin/hypercharge calculated?

[Harry235435]

I am familiar with the following equation which relates weak isospin (T₃) and weak hypercharge (Y_W):
Y_W = 2(Q-T₃)
(Where Q is electric charge)
However, while this can be used to calculate Y_W from T₃ and vice versa, how do you calculate each of these properties individually, without using the other?

 

[Jonathan Scott]

Weak isospin is assigned to the usual (left-handed chirality) leptons and quarks in such a way as to distinguish the two different charge states in each generation, in the same way that normal isospin distinguishes the up and down quarks. I think that for those particles T₃ = Q + L/2 - B/2 where Q is the charge, L is the lepton number and B is the baryon number.

There's a table of weak isospin and weak hypercharge for those particles in the Wikipedia article on weak hypercharge.