According to Stokes’ law, a perfect sphere traveling through a viscous liquid feels a drag force proportional to the frictional coefficient :
where  is the liquids viscosity,  is the spheres drift speed, and  is its radius. Because ionic mobility  is directly proportional to drift speed, it is inversely proportional to the frictional coefficient:
where  represents ionic charge in integer multiples of electron charges.
In 1905, Albert Einstein found the diffusion coefficient  of an ion to be proportional to its mobility constant:
where  is the Boltzmann constant and  is electrical charge. This is known as the Einstein relation. Substituting in the frictional coefficient of a perfect sphere from Stokes’ law yields
which can be rearranged to solve for , the radius:
In non-spherical systems, the frictional coefficient is determined by the size and shape of the species under consideration.