Define your project activities, dependencies, and durations. See the forward pass, backward pass, total float, free float, and critical path calculated instantly with a visual network diagram.
Project Duration
14 units
Critical Path
A → B → D → E
| ID | Name | Dur | ES | EF | LS | LF | TF | FF | CP |
|---|---|---|---|---|---|---|---|---|---|
| A | Start | 3 | 0 | 3 | 0 | 3 | 0 | 0 | ✓ |
| B | Design | 5 | 3 | 8 | 3 | 8 | 0 | 0 | ✓ |
| C | Prototype | 2 | 3 | 5 | 6 | 8 | 3 | 3 | |
| D | Test | 4 | 8 | 12 | 8 | 12 | 0 | 0 | ✓ |
| E | Launch | 2 | 12 | 14 | 12 | 14 | 0 | 0 | ✓ |
max(EF of all predecessors)Earliest an activity can begin (0 for starting activities)ES + DurationEarliest an activity can completemin(LS of all successors)Latest an activity can finish without delaying the projectLF - DurationLatest an activity can start without delaying the projectLS - ES = LF - EFHow long an activity can be delayed without impacting the project end datemin(ES of successors) - EFHow long an activity can be delayed without affecting any successorLongest path (TF = 0)Sequence of activities with zero total float that determines minimum project durationAdding resources to critical path activities to shorten their duration. Always targets activities with the lowest crash cost per unit of time saved. Increases cost but compresses the schedule.
Performing critical path activities in parallel that were originally planned sequentially. Increases risk (rework, defects) but can compress the schedule without adding cost. Only works when activities have separable components.
PMP Exam Tip
Schedule compression techniques only apply to the critical path. Crashing or fast-tracking non-critical activities does not reduce the project duration. If a question asks how to shorten the schedule, look for answers that target critical path activities first.
Total Float vs Free Float: Total Float measures delay tolerance relative to the project end date. Free Float measures delay tolerance relative to the next activity. Free Float is always less than or equal to Total Float.
Multiple Critical Paths: A project can have more than one critical path. When this happens, risk increases because a delay in any critical path delays the project.
Near-Critical Path: Activities with very low total float (e.g., 1-2 units) are near-critical. They deserve close monitoring because small delays can make them critical.
Zero-Duration Activities: Milestones have zero duration. They can appear on the critical path and help mark key deliverable dates.
The critical path is the longest sequence of dependent activities through the network diagram. It determines the shortest possible project duration — any slip on a critical-path activity slips the entire project.
Total float is how long an activity can be delayed without delaying the project end date. Free float is how long it can be delayed without delaying any successor activity. Free float is always less than or equal to total float.
The forward pass walks the network left to right to calculate Early Start (ES) and Early Finish (EF). The backward pass walks right to left to calculate Late Start (LS) and Late Finish (LF). Total float = LS − ES = LF − EF.
By definition, an activity is on the critical path when any delay to it delays project finish, which means it has no slack — its total float equals zero.
Expect several Process-domain questions on CPM calculation, identifying the critical path from a network diagram, schedule compression (crashing and fast-tracking), and interpreting float values.