Critical Path Method Calculator

List activities as id, duration, predecessors to find the critical path.

How it is calculated

Enter one activity per line as id, duration, predecessors, with commas between the three parts. List several predecessors in the third part separated by spaces, plus signs or semicolons (for example B C), and leave it empty for an activity that can start at time 0. The tool computes each activity's earliest finish: EF = max(EF of predecessors) + duration. The project duration is the largest EF. It then walks back from an activity that finishes last, always stepping to the predecessor with the latest EF, and prints that chain as the critical path. Durations can be in any single unit you choose (days, weeks) and may have decimals; the total is shown with only as many decimals as needed (7.75, not 8). A negative or non-numeric duration gives no result. If two chains tie, only one is listed (the first found). No slack values are reported.

Worked example

Five tasks: A takes 3 and has no predecessor; B takes 4 after A; C takes 2 after A; D takes 5 after both B and C; E takes 2 after D. Earliest finishes: A = 3, B = 3 + 4 = 7, C = 3 + 2 = 5, D = max(7, 5) + 5 = 12, E = 12 + 2 = 14. The project duration is 14 across 5 activities. Walking back from E, the latest predecessor each time gives A → B → D → E. Task C is not on the path because B finishes later, so C could slip by up to 2 units without moving the end date.

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Common mistakes

  • Separating the three parts with spaces instead of commas: a line like B 4 A is skipped, so the task is missing from the count and from the path.
  • Separating multiple predecessors with commas: the comma starts a new field, so D,5,B,C only registers B. Write D,5,B C.
  • Misspelling a predecessor id; an id that does not exist is ignored, so the task silently starts at time 0 and the project can come out too short.
  • Creating a loop, such as A after B and B after A. A network with a loop has no critical path, so the tool shows no result; check that the network flows in one direction.
  • Assuming ties are shown: when two paths have equal length, only the first found is listed, although both are critical.

About this calculator

The critical path method builds a network of project activities with their durations and dependencies (predecessors), then runs a forward pass to find each activity's earliest possible finish. The longest sequence through the network is the critical path: it sets the minimum possible project duration, and delaying any activity on it delays the whole project. A full CPM analysis also runs a backward pass to find latest allowable times and the slack of each activity; this calculator does not compute slack, it gives the total duration, the critical path and the number of activities.

You list one activity per line as id, duration, predecessors. Project managers, especially in construction, engineering, and software delivery, use CPM to identify which tasks can't slip without delaying the whole project and to focus monitoring and resources on those critical activities.

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