Oseen considered the sphere to be stationary and the fluid to be flowing with a flow velocity () at an infinite distance from the sphere. Inertial terms were neglected in Stokes' calculations. It is a limiting solution when the Reynolds number tends to zero. When the Reynolds number is small and finite, such as 0.1, correction for the inertial term is needed. Oseen substituted the following flow velocity values into the Navier-Stokes equations.
Inserting these into the Navier-Stokes equations and neglecting the quadratic terms in the primed quantities leads to the derivation of Oseen's approximation:
Since the motion is symmetric with respect to  axis and the divergence of the vorticity vector is always zero we get:
the function  can be eliminated by adding to a suitable function in , is the vorticity function, and the previous function can be written as:
and by some integration the solution for  is:
thus by letting  be the "privileged direction" it produces:
then by applying the three boundary conditions we obtain
the new improved drag coefficient now become:
and finally, when Stokes solution was solved on the basis of Oseens approximation, it showed that the resultant drag force is given by
where:
*  is the Reynolds number based on the radius of the sphere, 
*  is the hydrodynamic force
*  is the flow velocity
*  is the fluid viscosity
The force from Oseen's equation differs from that of Stokes by a factor of