We introduce a new quantum gravitational force $F_{PN}=\frac{G_N \hbar}{c}\frac{m}{r^3}$ by using the fundamental constants, like $\hbar$, $c$, $G_N$, where $G_N$, $\hbar$ and $c$ are the Newtonian, the Planck constants and velocity of light. It turns out that conditions of equalities of this force with the Newtonian, the strong interacting-Yukawa type forces give exact physical meaning of the Planck length and the Compton length of a wave. Moreover, equality conditions of this force with the Coulomb and the Dirac magnetic monopole's forces give rise to introduce the concept of the running coupling constant $\alpha(E)=\alpha \ln (1+\frac{E}{\mu})$ and to obtain mass formula $M_{mon}=M_{Pl}\frac{1}{\sqrt{\alpha}}$ for a magnetic monopole, where $\alpha=\frac{e^2}{\hbar c}$ is the fine structure constant. Physical meaning of the vacuum energy is also considered.