The $B_c$ mass up to order $α_s^4$

We evaluate in perturbative QCD, up to order $\alpha_s^4$, the mass of the $B_c$. We use the so-called 1S-mass in order to improve the convergence of the perturbative series. Our result is $E(B_c)_{pert} = 6323^{+3 +7}_{-1 -6}$ MeV. Non-perturbative effects are discussed. An estimate in terms of local condensates and a comparison with potential models seem to be consistent with non-perturbative contributions of the order $ - (40\div 80)$ MeV.