Nuclear spin is an intrinsic angular momentum that is quantized. This means that the magnitude of this angular momentum is quantized (i.e. S can only take on a restricted range of values), and also that the x, y, and z-components of the angular momentum are quantized, being restricted to integer or half-integer multiples of ħ. The integer or half-integer quantum number associated with the spin component along the z-axis or the applied magnetic field is known as the magnetic quantum number, m, and can take values from +S to −S, in integer steps. Hence for any given nucleus, there are a total of  angular momentum states.
The z-component of the angular momentum vector () is therefore , where ħ is the reduced Planck constant. The z-component of the magnetic moment is simply: