Note that the electric force between two charges is 
$$F_{\rm elec}=\frac{q_1q_2}{4\pi\epsilon_0 r^2},$$
the gravitational force is 
$$F_{\rm grav}=G\frac{M_1M_2}{r^2},$$
and finally the (maximal) force for two dipoles is 
$$F_{\rm mag}= \frac{3\mu_0 |\mathbf m_1|| \mathbf m_2|}{2\pi r^4},$$
where $\mathbf m_1,\mathbf m_2$ are the magnetic dipole moments.


On the same grounds as the standard electric and gravitational parameters, can just forget about the distance dependence and you just you define a standard magnetic parameter by multiplying the magnetic field constant by the dipole moment $\mathbf m$: $$\mu_{\rm mag}=\frac{\mu_0}{4\pi}|\mathbf m|\;\text{or}\;\frac{3\mu_0}{2\pi}|\mathbf m|$$.