In magnetohydrodynamics, the magnetic Reynolds number (R) is a dimensionless quantity that estimates the relative effects of advection or induction of a magnetic field by the motion of a conducting medium to the magnetic diffusion. It is the magnetic analogue of the Reynolds number in fluid mechanics and is typically defined by:
where
*  is a typical velocity scale of the flow,
*  is a typical length scale of the flow,
*  is the magnetic diffusivity.
The mechanism by which the motion of a conducting fluid generates a magnetic field is the subject of dynamo theory.  When the magnetic Reynolds number is very large, however, diffusion and the dynamo are less of a concern, and in this case
focus instead often rests on the influence of the magnetic field on the flow.