In project management, the critical path in a network diagram is the sequence of tasks or activities that must be completed on time in order to complete the project on schedule. It is the longest path through the network diagram and represents the minimum amount of time required to complete the project.

Tasks or activities on the critical path have zero float or slack, which means that any delay in their completion will cause a delay in the overall project schedule. This makes the critical path an important factor to consider when planning and managing a project. By identifying the critical path, project managers can focus their efforts on managing the tasks and activities that are most critical to the project's success and ensuring that they are completed on time.

In order to calculate the critical path, project managers need to identify all of the tasks or activities in the project and their dependencies, and then determine the duration of each task. They can then use this information to create a network diagram and calculate the critical path using techniques such as the Program Evaluation and Review Technique (PERT) or the Critical Path Method (CPM).