For a circular coil with anticlockwise current, the magnetic field at its center is determined by the right-hand thumb rule. Curl your fingers in the direction of the current; your thumb points in the direction of the magnetic field. Since the coil is circular and the field at the center is perpendicular to its plane, the direction is straight out of the plane.

Mathematically, the field magnitude is $B=\frac{{\mu }_{0}I}{2R}$, but the direction is given by the right-hand rule.

Final Answer: Perpendicular to the plane of coil