In this paper, we shall show Kantorovich type inequalities for the difference with two negative parameters as follows: Let $A$ and $B$ be positive invertible operators on a Hilbert space $H$ such that $MI \ge A \ge mI$ for some positive numbers $M >m>0$. If the usual order $A \ge B$ holds, then $$B^q+ C(m,M,p,q)I \ge B^q+C\left(\frac{1}{M}, \frac{1}{m}, -p,-q\right)I \ge A^p \qquad \mbox{for all $p,q<-1$,}$$ where $C(m,M,p,q)$, the Kantorovich constant for the difference with two parameters, is defined as $$ (q-1)\left\{\frac{M^p -m^p}{q(M-m)}\right\}^{\frac{q}{q-1}} + \frac{m^pM-mM^p}{M-m} \quad \mbox{if} \quad m \le \left\{\frac{M^p-m^p}{q(M-m)}\right\}^{\frac{1}{q-1}} \le M. $$ As applications, we show some characterizations of the chaotic order. Thereby, we observe the difference between the usual order and the chaotic one by virtue of Kantorovich constant for the difference.