An easy way to see how the Planck length arises naturally is as follows. h-bar×c is a natural quantity of force×area, or equivalently of energy×length, which is present in all light. It is, for example, the product of each photon's energy multiplied by its vacuum angular wavelength. Playing a central role in gravity, on the other hand, is a constant force c4/G. Among other things this force is the central coefficient in the Einstein equation relating energy-momentum density to curvature. This is the natural unit or Planck force—that giving unit acceleration to unit mass in the Planck system—and it is basic to the prevailing model, General Relativity, of how gravity works.
Simply dividing the natural force×area unit (h-bar×c) by the natural unit force (c4/G) gives the natural or Planck unit of area, h-barG/c3. The square root of this, namely (h-barG/c3)½, is the Planck length.
The CODATA recommended value for the length, lPlanck, is 1.6160×10-35 meter with estimated uncertainty of about 1/13 of a percent.
Physicist John Baez has suggeted that the Planck area
h-barG/c3 is even more fundamental than the Planck length,
which is its square root. A webpage at John Baez's site gives a cogent account
of some of the current interest surrounding the Planck length.
http://math.ucr.edu/home/baez/planck/node2.html