The critical path method (also, critical path method) is an algorithm used to calculate times and deadlines in project planning.[1]​

This calculation system, known by its acronym CPM (Critical Path Method), was developed in 1957 in the United States of America, by an operations research center for the firms Dupont and Remington Rand, seeking control and optimization of costs through adequate planning and programming of the component activities of the project. Another important project of that time, the "Polaris" missile project, led in 1958 to the creation of one of the critical path programming methods, known as PERT (Program Evaluation and Review Technique).[2]​.

In project administration and management, a critical path is the sequence of the terminal elements of the project network with the longest duration between them, determining the shortest time in which it is possible to complete the project. The duration of the critical path determines the duration of the entire project. Any delay in an element of the critical path affects the planned completion date of the project, and there is said to be no slack in the critical path.

A project can have several parallel critical paths. An additional parallel path through the network with the total duration close to that of the critical path, although necessarily shorter, is called a sub-critical path.

Originally, the critical path method considered only dependencies between terminal elements. A related concept is the critical chain, which adds resource dependencies. Each resource depends on the manager at the time where the critical path occurs.

Unlike the program evaluation and review technique (PERT), the critical path method uses deterministic times, while PERT uses probabilistic times from three estimates. However, developing a project based on CPM and PERT networks are similar and consist of:

In practical terms, the critical path is interpreted as the maximum dimension that the project can last and the differences with the paths other than the critical path are called slack times.