This paper deals with defining the concept of agent-based time delay margin and computing its value in multi-agent systems controlled by event-triggered based controllers. The agent-based time delay margin specifying the time delay tolerance of each agent for ensuring consensus in event-triggered controlled multi-agent systems can be considered as complementary for the concept of (network) time delay margin, which has been previously introduced in some literature. In this paper, an event-triggered control method for achieving consensus in multi-agent systems with time delay is considered. It is shown that the Zeno behavior is excluded by applying this method. Then, in a multi-agent system controlled by the considered event-triggered method, the concept of agent-based time delay margin in the presence of a fixed network delay is defined. Moreover, an algorithm for computing the value of the time delay margin for each agent is proposed. Numerical simulation results are also provided to verify the obtained theoretical results.