Scheduling
The critical path method (CPM), step by step
The critical path is the chain of activities that sets the finish date. This guide shows how it is calculated, with a four-activity example you can check by hand.
What the critical path is
A schedule is a network: activities, their durations, and the links that say what must happen before what. The critical path is the longest chain through that network. Its length is the shortest time the project can take, and a day lost on any activity in the chain is a day lost on the finish date.
Activities off the critical path have float: they can slip a little without moving the finish. Knowing which activities have float, and how much, is what lets a project manager decide where to put attention.
The two passes
Forward pass. Start at the beginning. Each activity's early start (ES) is the latest early finish of the activities before it. Its early finish (EF) is ES plus its duration. The largest EF is the project duration.
Backward pass. Start at the end. Each activity's late finish (LF) is the earliest late start of the activities after it. Its late start (LS) is LF minus its duration.
| ES | the largest EF of the predecessors |
|---|---|
| EF = ES + D | early finish |
| LF | the smallest LS of the successors |
| LS = LF − D | late start |
| TF = LS − ES | total float: slip allowed before the finish moves |
| FF | free float: slip allowed before the next activity moves |
A worked example
Four activities, in working days. Procurement and permits both start when design ends, and installation needs both.
| Activity | Duration | After | ES | EF | LS | LF | Total float |
|---|---|---|---|---|---|---|---|
| A · Design | 5 | — | 0 | 5 | 0 | 5 | 0 |
| B · Procure | 10 | A | 5 | 15 | 5 | 15 | 0 |
| C · Permits | 4 | A | 5 | 9 | 11 | 15 | 6 |
| D · Install | 3 | B, C | 15 | 18 | 15 | 18 | 0 |
The path A, B, D is 5 + 10 + 3 = 18 days. The path A, C, D is 5 + 4 + 3 = 12 days. The project takes 18 days, and A, B and D are critical: their total float is zero. Permits can slip up to 6 days before the finish moves.
Now stretch permits from 4 days to 12. The second path becomes 5 + 12 + 3 = 20 days, the finish moves to day 20, and the critical path jumps: permits are critical and procurement has 2 days of float. That jump is why the critical path has to be recalculated after every update. You can try this on the live demo on our home page.
What real schedules add
- Four link types. Finish-to-start is the usual one. Start-to-start, finish-to-finish and start-to-finish let activities overlap.
- Lags and leads. A wait between two activities, such as seven days for concrete to cure, or an overlap.
- Calendars. Durations count working days, so weekends, holidays and shifts change the dates without changing the logic.
- Constraints. "Not earlier than" and "must finish by" dates. A deadline earlier than the calculated finish produces negative float: the schedule is already late.
- Progress. Once work starts, the calculation runs from the data date using remaining durations.
Five mistakes that break a critical path
- Open ends. An activity with no successor has float to the end of the project and hides delay.
- Hard constraints everywhere. Fixed dates override the logic, so the schedule stops predicting.
- Long lags. A 30-day lag is an activity nobody named. Model it as one.
- Very long activities. A six-month bar cannot be measured. Split it into pieces you can check.
- Stale progress. A schedule that is not updated to the data date shows last month's critical path.
The DCMA 14-point assessment measures most of these. Critova runs it on every schedule and lists the activities that fail each check.
Common questions
Can a project have more than one critical path?
Yes. Two chains of the same length are both critical, and near-critical paths with a few days of float deserve almost as much attention.
What is the difference between total float and free float?
Total float is how far an activity can slip before the project finish moves. Free float is how far it can slip before the next activity moves.
Is the critical path the same as the longest path?
Without constraints, yes. With constraints, activities can show zero or negative float without being on the longest chain, which is why tools report both.
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