CPM Calculator

The Critical Path Method (CPM) is the scheduling technique behind tools like Primavera P6 and Microsoft Project. From a list of activities, their durations and dependencies, it calculates the earliest and latest times each activity can happen, how much float each has, and which chain of activities determines the project's finish date.

How to use the calculator

1. Enter each activity with an ID, duration and its predecessors.
2. Run the calculation.
3. Review early start (ES), early finish (EF), late start (LS), late finish (LF) and total float for each activity, and the critical path.

How CPM works

• Forward pass: ES of an activity = the largest EF of its predecessors. EF = ES + duration.
• Backward pass: LF = the smallest LS of its successors. LS = LF - duration.
• Total float: LS - ES (or LF - EF). Activities with zero float are critical.

Worked example

Activities: A (3 days), B (5 days, after A), C (2 days, after A), D (4 days, after B and C). Forward pass: A 0 to 3, B 3 to 8, C 3 to 5, D 8 to 12. Project duration is 12 days. Backward pass gives C a late finish of 8, so its float is 8 - 5 = 3 days. The critical path is A, B, D.

Why it matters

• A delay to any critical activity delays the whole project by the same amount.
• Speeding up a non-critical activity does not shorten the project.
• To compress the schedule, add resources to critical activities (crashing) or run them in parallel (fast tracking).