Magnetophoresis--the motion of magnetic particles under applied magnetic gradient--is a process of great interest in novel applications of magnetic nanoparticles and colloids. In general, there are two main different types of magnetophoresis processes: cooperative magnetophoresis (a fast process enhanced by particle-particle interactions) and noncooperative magnetophoresis (driven by the motion of individual particles in magnetic fields). In the case of noncooperative magnetophoresis, we have obtained a simple analytical solution which allows the prediction of the magnetophoresis kinetics from particle characterization data (size and magnetization). Our comparison with new experimental results shows good quantitative agreement. In addition, we show the existence of a universal curve onto which all experimental results should collapse after proper rescaling. The range of applicability of the analytical solution is discussed in light of the predictions of a magnetic aggregation model [Soft Matter 7, 2336 (2011)].