Purpose <p>This paper proposes an efficient computational method for quantifying the transient characteristics of trajectories in nonlinear dynamical systems.</p> Methods <p>The point mapping under cell reference provides an efficient method for the computation of attractors and the basins of attraction. The key idea of this method is to record the attractors corresponding to the initial conditions and utilize the cell reference frame to rapidly find the state in close proximity to the current state from the computation-completed trajectories. In this paper, the method is improved to allow for the computation of the quantitative transient characteristics of initial conditions.</p> Results <p>The failure time and return time of initial conditions of various nonlinear dynamical systems are calculated using the method of point mapping under cell reference, and the results are compared with those obtained using the traditional point mapping method. The findings indicate that the proposed method can substantially reduce the calculation time while maintaining high accuracy.</p> Conclusion <p>The improved method of point mapping under cell reference can effectively quantify the transient characteristics of nonlinear dynamical systems.</p>