Critical Path Calculator (CPM with Float)

How it works

Forward pass: ES = max(EF of predecessors), EF = ES + duration · Project duration = max EF · Backward pass: LF = min(LS of successors), LS = LF − duration · Total float = LS − ES · Critical tasks have zero float

The critical path method (CPM), developed by DuPont and Remington Rand in the late 1950s, finds the longest chain of dependent tasks through a project network. That chain sets the shortest possible project duration: any delay to a critical task delays the whole project, while tasks with float can slip by that amount without affecting the end date. The forward pass computes the earliest start and finish of each task, the backward pass the latest, and their difference is the total float — the approach described in the PMI PMBOK Guide schedule-management chapter.

Worked example

With tasks A=3, B=4 after A, C=2 after A, D=5 after B and C, E=2 after C and F=3 after D and E, the forward pass gives D an early start of 7 (after B finishes) and F an early start of 12, so the project takes 15 days. The critical path is A → B → D → F. Task C has 2 days of float and task E has 5 days, the most of any task.

Sources: Critical path method — forward and backward pass · Float (project management) — total and free float

Frequently asked questions