  We derive the formula of the black hole entropy with a minimal length of the
Planck size by counting quantum modes of scalar fields in the vicinity of the
black hole horizon, taking into account the generalized uncertainty principle
(GUP). This formula is applied to some intriguing examples of black holes - the
Schwarzschild black hole, the Reissner-Nordstrom black hole, and the
magnetically charged dilatonic black hole. As a result, it is shown that the
GUP parameter can be determined by imposing the black hole entropy-area
relationship, which has a Planck length scale and a universal form within the
near-horizon expansion.
