On the axis at distance $x$ from center: $B = \frac{\mu_0 IR^2}{2(R^2 + x^2)^{3/2}}$. At the center ($x = 0$): reduces to $\mu_0 I/(2R)$. Far from the loop ($x \gg R$): $B \approx \mu_0 m/(2\pi x^3)$ where $m = IA = I\pi R^2$ is the magnetic dipole moment. This is identical in form to the electric dipole field along the axis. The field on the axis is always along the axis direction.