Calculations are presented of the axial charge gA in models where relativistic quarks are confined by arbitrary vector potentials, scalar potentials ~ rn and scalar-vector potentials ~ 1/2(1+γ0)rn for arbitrary n >= 0. It is shown that gA vanishes for all vector potentials and is a monotonically decreasing function of the exponent n for scalar and scalar-vector potentials. The non-relativistic value 5/3 is reproduced (for n = 0) as well as the MIT bag model value 1.09 (for n --> ∞) they are upper and lower limits of gA, respectively. This function gA (n) is shown not to depend on the quark confinement size (i.e. gA is scale invariant), but only depends on the type of confinement (scalar, vector). Acceptable values for gA are found with ns = 2-3 (scalar) and ns-v = 0.5-0.7 (scalar-vector).