Interrupt and context switch are basic mechanisms for multi-task scheduling in real-time and embedded systems. During schedulability analysis, the overheads of the interrupt and context switch should be considered in the calculation of tasks' worst-case response time. The current calculation methods of response time add interrupt as task with high priority, and simply add the overheads of context switch in the meantime. However, these methods neglect the details of practical systems and roughly give an inaccurate worst-case response time. In this paper, the mechanisms and time flow of interrupt and context switch are thoroughly described. In addition, their influence on tasks' critical instant is discussed. More importantly, a much more accurate calculation method for response time is presented. At last, simulations is conducted to validate the improvement in accuracy of this new method. The response time analysis accounting for scheduling overheads is extended in this paper for the resource-constrained hard real-time systems which need to accurately calculate the response time.