text: 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.