According to Lord Kelvin's equation of 1871,
If the particle is assumed to be spherical, then ; hence,
Note: Kelvin defined the surface tension  as the work that was performed per unit area by the interface rather than on the interface; hence his term containing  has a minus sign.  In what follows, the surface tension will be defined so that the term containing  has a plus sign.
Since , then ; hence,
Assuming that the vapor obeys the ideal gas law, then
where:
: = mass of a volume  of vapor
: = molecular weight of vapor 
: = number of moles of vapor in volume  of vapor
: = Avogadro constant
: = ideal gas constant = 
Since  is the mass of one molecule of vapor or liquid, then
: volume of one molecule  .
Hence
: where  .
Thus
Since
then
Since  , then  . If , then . Hence
Therefore
which is the Ostwald–Freundlich equation.