The defining equation of capacitance is
or Capacitance = Charge per unit Voltage. Capacitance is constant within certain limits, and is a feature of the construction of the capacitor.
The simplest capacitor is the parallel plate capacitor, which consists of two conducting plates connected to a potential difference.
If the charge density on each plate is
then
Apply Gauss's Divergence theorem to each plate:
since the field
exists only between the plates and is uniform there, and the total charge enclosed by the volume of the plate is
This equation simplifies to
and since
we have
hence
gives the capacitance of a parallel plate capacitor.