The in-plane nearest-neighbor Heisenberg magnetic coupling constant, J , of La 2 CuO 4 , Nd 2 CuO 4 , Sr 2 CuO 2 Cl 2 , YBa 2 Cu 3 O 6 , and undoped HgBa 2 Ca n − 1 Cu n O 2 n + 2 + δ ( n = 1 , 2 , 3 ) is calculated from accurate ab initio configuration interaction calculations. For the first four compounds, the theoretical J values are in quantitative agreement with experiment. For the Hg-based compounds the predicted values are − 135 meV ( n = 1 ) and ∼ − 160 meV ( n = 2 , 3 ), the latter being much larger than in previous cases and, for n = 3 , increasing with pressure. Nevertheless, the physics governing J in all these layered cuprates appears to be the same. Moreover, calculations suggest a possible relationship between J and T c .