In the theory of magnetohydrodynamics, the magnetic Reynolds number can be derived from the induction equation:
where
*  is the magnetic field,
*  is the fluid velocity,
*  is the magnetic diffusivity.
The first term on the right hand side accounts for effects from magnetic induction in the plasma and the second term accounts for effects from magnetic diffusion. The relative importance of these two terms can be found by taking their ratio, the magnetic Reynolds number . If it is assumed that both terms share the scale length  such that  and the scale velocity  such that , the induction term can be written as
and the diffusion term as
The ratio of the two terms is therefore