Critical Path Method (CPM): The Step-by-Step Guide
Master the essential project management technique to identify the longest sequence of dependent tasks and determine the shortest possible time to complete your project.
How to Calculate the Critical Path
Step 1: The Forward Pass (Early Dates)
Determines the Earliest Start (ES) and Earliest Finish (EF) for each task.
- ✓ Formula: EF = ES + Duration
- ✓ Start with the first task at ES = 0.
- ✓ If a task has multiple predecessors, use the highest EF of the previous tasks.
Step 2: The Backward Pass (Late Dates)
Determines the Latest Finish (LF) and Latest Start (LS) without delaying the project.
- ✓ Formula: LS = LF - Duration
- ✓ Start from the last task and work backwards.
- ✓ If a task has multiple successors, use the lowest LS.
Step 3: Calculate Total Float (Slack)
Formula: Float = LS - ES (or LF - EF)
Tasks with zero float are on the Critical Path. Any delay in these tasks will delay the entire project.
Don't do the math manually!
Use our free tool to automatically calculate your project's Forward Pass, Backward Pass, and Total Float.
Open Free CPM Calculator →What Is the Critical Path Method?
The critical path method (CPM) is a scheduling technique that finds the longest sequence of dependent activities in a project. That sequence is the critical path, and its total duration is the shortest possible time to finish the project. CPM was developed in the late 1950s for large engineering projects and is now a core part of the PMBOK Guide's schedule management processes.
CPM answers three practical questions: how long the project will take, which activities cannot slip without moving the end date, and how much flexibility every other activity has. That flexibility is called float, or slack.
Key Terms You Need to Know
- Early Start (ES): the earliest day an activity can begin once all its predecessors are finished.
- Early Finish (EF): ES plus the activity's duration.
- Late Start (LS): the latest day an activity can begin without delaying the project.
- Late Finish (LF): the latest day an activity can finish without delaying the project.
- Total float: LS minus ES (or LF minus EF). The time an activity can slip before the project end date moves.
- Free float: the time an activity can slip before it delays the early start of any successor.
- Critical activity: an activity with zero total float.
Worked Example: Finding the Critical Path
Here is a small IT project with six activities. This example uses the convention that the first activity starts on day 0, so EF = ES + duration.
| Activity | Description | Duration (days) | Predecessor | ES | EF | LS | LF | Total float | Critical? |
|---|---|---|---|---|---|---|---|---|---|
| A | Gather requirements | 3 | - | 0 | 3 | 0 | 3 | 0 | Yes |
| B | Design solution | 4 | A | 3 | 7 | 3 | 7 | 0 | Yes |
| C | Order hardware | 2 | A | 3 | 5 | 7 | 9 | 4 | No |
| D | Build and configure | 5 | B | 7 | 12 | 7 | 12 | 0 | Yes |
| E | Install hardware | 3 | C | 5 | 8 | 9 | 12 | 4 | No |
| F | Test and hand over | 2 | D, E | 12 | 14 | 12 | 14 | 0 | Yes |
Forward pass
Start A at day 0, so it finishes on day 3. B and C both depend on A, so both start on day 3: B finishes on day 7 and C on day 5. D follows B (7 to 12) and E follows C (5 to 8). F needs both D and E, so it waits for the later one: F starts on day 12 and finishes on day 14. The project takes 14 days.
Backward pass
Start from F with LF = 14, so LS = 12. D and E must both finish by day 12, which gives D an LS of 7 and E an LS of 9. B must finish by D's LS (7), so its LS is 3. C must finish by E's LS (9), so its LS is 7. A feeds both B and C, so it takes the smaller LS of the two (3), giving A an LS of 0.
Float and the critical path
A, B, D and F have zero float, so the critical path is A, B, D, F and it takes 14 days. C and E each have 4 days of total float. Look closely at C: its free float is 0, because any slip pushes E's early start. E has 4 days of free float, because F cannot start before day 12 anyway. This is why the PMP exam tests the difference between total and free float.
How to Shorten the Critical Path
If the 14-day schedule is too long, you can only shorten it by working on critical activities. Shortening C or E achieves nothing until their float is used up. The two standard techniques are:
- Crashing: adding resources to a critical activity to finish it sooner. It costs more, so crash the activity with the lowest cost per day saved first.
- Fast tracking: running activities in parallel that were planned in sequence, such as starting some of the build work before design is fully signed off. It adds rework risk rather than cost.
After every change, recalculate. Shortening one path can make a different path critical. For a full walkthrough with cost figures, see our guide to schedule compression techniques.
CPM vs PERT
CPM uses a single, fixed duration for each activity, which suits work you have done before. PERT uses three estimates (optimistic, most likely and pessimistic) and combines them as (O + 4M + P) / 6 to reflect uncertainty. Many schedules use PERT estimates to set the durations and then run CPM to find the critical path. Our guide to estimation techniques covers PERT in detail.
Common Mistakes
- Taking the lowest EF instead of the highest when an activity has several predecessors.
- Taking the highest LS instead of the lowest during the backward pass.
- Mixing day-0 and day-1 conventions in the same calculation.
- Ignoring near-critical paths with only a day or two of float. They become critical after a small delay.
- Treating the critical path as fixed. Update it whenever durations or dependencies change.
Frequently Asked Questions
What is the critical path in simple terms?
It is the longest chain of dependent activities from the start of a project to the end. Its length is the shortest time the project can take, and any delay to an activity on it delays the finish date.
Can a project have more than one critical path?
Yes. If two or more paths have the same, longest duration, they are all critical. This makes the schedule riskier, because a delay on any of them moves the end date.
What is the difference between total float and free float?
Total float is how long an activity can slip without delaying the project. Free float is how long it can slip without delaying the early start of the next activity. Free float is always less than or equal to total float.
Can float be negative?
Yes. Negative float means the schedule already misses a required date, such as a contractual deadline. You need to compress the schedule or renegotiate the date.
Is the critical path method still tested on the PMP exam?
Yes. Expect questions that ask you to find the critical path, calculate float, or choose between crashing and fast tracking when the schedule slips.