The critical path and float times
Identifying the critical path
- The critical path is the longest path through the network from start to finish. Its length is the project duration.
- An activity is critical when it has zero float. Three conditions must hold together for the activity from node to node :
- — its start event is critical
- — its end event is critical
- its duration — there is no gap to absorb delay
- The third condition is essential. Two critical events can be joined by an activity that still has float, if a longer route runs between them.
- The critical path is a continuous chain from start to finish. If your critical activities have a gap, one of them has been misclassified.
- There can be more than one critical path, and long projects usually have several. Report them all.
The four activity times
For an activity of duration running from node to node :
| Quantity | Formula | Meaning |
|---|---|---|
| Earliest start | soonest it can begin | |
| Earliest finish | soonest it can be done | |
| Latest finish | last moment it may end | |
| Latest start | last moment it may begin |
- Set these out in a table, one row per activity. Every float comes straight out of it.
Total float
- In words: the time available for the activity, minus the time it needs.
- It is the amount the activity can be delayed or extended without delaying the PROJECT.
- Total float is zero exactly for critical activities, which gives a second way to find the critical path.
- Total float is shared. Two activities in the same chain may each show 3 days of total float, but the chain has 3 days in total — using it on one consumes it for the other.
Free float
- The amount an activity can be delayed without delaying any FOLLOWING activity's earliest start.
- Free float is genuinely the activity's own. Using it affects nothing else.
- Free float is never greater than total float, and is often smaller. The difference is called interfering float — time that can be used, but only by pushing a later activity out of its earliest slot.
Which float to use
| The question asks | Use |
|---|---|
| "Can this be delayed without the project finishing late?" | Total float |
| "Can this be delayed without disturbing anything downstream?" | Free float |
| "Which activities must be watched?" | Those with zero total float — the critical path |
- A good report states both, and says whether the float is private (free) or shared with a chain (total).
Reading the results in context
- The critical activities are where management attention goes. Delay there is delay to the project, one day for one day.
- Non-critical activities are where flexibility lives. They can be rescheduled to smooth out demand for people, machines or money.
- Shortening a non-critical activity does nothing. Only shortening a critical activity can shorten the project — and only until a different path becomes critical.
- Say all of this in the context's own language: "the handrail crew can start up to two days late without pushing back the opening, but the framing crew cannot slip at all."
Worked ExampleFloats for the deck project
Using the deck project's event times, build the full activity table, find the critical path, and state the total and free float for every activity.
Event times from both passes:
| Node | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| Earliest | 0 | 3 | 8 | 7 | 13 | 20 | 23 | 25 | 26 |
| Latest | 0 | 3 | 11 | 7 | 13 | 20 | 25 | 25 | 26 |
Step 1 — List each activity with its nodes and duration
| Activity | From | To | Duration |
|---|---|---|---|
| A | 1 | 2 | 3 |
| B | 2 | 3 | 5 |
| C | 2 | 4 | 4 |
| D | 4 | 5 | 6 |
| E | 3 | 5 | 2 |
| F | 5 | 6 | 7 |
| G | 6 | 8 | 5 |
| H | 6 | 7 | 3 |
| J | 8 | 9 | 1 |
Step 2 — Compute the four times for each activity
Earliest start ; earliest finish ; latest finish ; latest start .
| Activity | ||||
|---|---|---|---|---|
| A | 0 | 3 | 3 | 0 |
| B | 3 | 8 | 11 | 6 |
| C | 3 | 7 | 7 | 3 |
| D | 7 | 13 | 13 | 7 |
| E | 8 | 10 | 13 | 11 |
| F | 13 | 20 | 20 | 13 |
| G | 20 | 25 | 25 | 20 |
| H | 20 | 23 | 25 | 22 |
| J | 25 | 26 | 26 | 25 |
Step 3 — Compute total float,
| Activity | Total float | |
|---|---|---|
| A | 0 | |
| B | 3 | |
| C | 0 | |
| D | 0 | |
| E | 3 | |
| F | 0 | |
| G | 0 | |
| H | 2 | |
| J | 0 |
Step 4 — Compute free float,
| Activity | Free float | |
|---|---|---|
| A | 0 | |
| B | 0 | |
| C | 0 | |
| D | 0 | |
| E | 3 | |
| F | 0 | |
| G | 0 | |
| H | 0 | |
| J | 0 |
Step 5 — Identify the critical path
Activities with zero total float: A, C, D, F, G, J.
Check the chain is continuous:
Unbroken from start to finish ✓
Check the length:
Step 6 — Note the difference between the two floats
B and E each show 3 days of total float — but:
- B's free float is 0. Delaying B pushes E out of its earliest start, even though the project still finishes on time.
- E's free float is 3. Delaying E by up to 3 days disturbs nothing at all.
H shows 2 days of total float but 0 days of free float, since .
Step 7 — Report to the site manager
Where the flexibility is:
- Ordering and delivering materials (B and E) share 3 days of slack. The order can be placed up to 3 days late, or the delivery can arrive up to 3 days after its earliest date — but not both.
- Handrails (H) can be delayed up to 2 days without affecting the inspection date.
Where it is not:
- Foundations (D, 6 days) and framing (F, 7 days) are the longest critical activities. They carry the greatest risk simply by being longest: a day of rain during either costs a day on the whole project.
- Speeding up the materials chain achieves nothing. Materials already arrive 3 days before they are needed, so paying for express delivery would buy no time at all.