At terminal (or settling) velocity, the excess force  due to the difference between the weight and buoyancy of the sphere (both caused by gravity) is given by:
where (in SI units):
* is the mass density of the sphere [kg/m]
* is the mass density of the fluid [kg/m]
* is the gravitational acceleration [m/s]
Requiring the force balance  and solving for the velocity  gives the terminal velocity . Note that since the excess force increases as  and Stokes' drag increases as , the terminal velocity increases as  and thus varies greatly with particle size as shown below. If a particle only experiences its own weight while falling in a viscous fluid, then a terminal velocity is reached when the sum of the frictional and the buoyant forces on the particle due to the fluid exactly balances the gravitational force. This velocity  [m/s] is given by:
where (in SI units):
*  is the gravitational field strength [m/s]
*  is the radius of the spherical particle [m]
*  is the mass density of the particle [kg/m]
*  is the mass density of the fluid [kg/m]
*  is the dynamic viscosity [kg/(m•s)].