We study the trajectories and escaping problem in the Hénon-Heiles system using a new fourth order symplectic algorithm and the Runge-Kutta-Fehlberg algorithm. Starting from the same initial point，we found the distance between the two numerical trajectories calculated by the two algorithms increases exponentially in time in the chaotic region. We show this result can be used to measure chaos. We also calculate the escape rate as a function of energy above threshold in the Hénon-Heiles system. The results calculated with two different algorithms agree very well.