Critical Path and Float on the PMP Exam
Most PMP questions ask for judgment. You read a situation, weigh a few reasonable-sounding actions, and choose the one a competent project manager would take. Reasonable people can disagree about those, and candidates lose points on them in ways that are hard to predict.
Schedule network questions are different. They have one right answer, and the answer follows from arithmetic you can do on the erasable board in about ninety seconds. There is no judgment to second-guess. That makes them some of the most reliable points available on the exam, and it is worth being fully fluent rather than roughly familiar.
The PM PrepCast, describing how these items are typically built, notes that sample questions present around five to ten activities and expect you to calculate dates and float by hand. That is the scale to practice at.
What the critical path actually is
PMI's own scheduling literature defines the critical path as the continuous string of critical activities between the start and finish of the project — the sequence where any delay pushes out project completion directly.
Two consequences follow, and both are tested:
- The critical path is the longest path through the network, not the shortest. It is longest in duration, and that length is the minimum time the project can take.
- Activities on the critical path have zero total float. There is no slack to absorb a delay.
The word "critical" is where candidates trip. It does not mean important, high-risk, or high-visibility. A trivial two-day task can sit on the critical path while the most technically demanding work in the project sits off it with a week of slack. The exam will sometimes describe an activity in language that makes it sound essential precisely to see whether you will calculate or react.
The forward pass and the backward pass
Every float number comes out of two sweeps through the network.
The forward pass runs left to right and produces the earliest each activity can happen. Early Finish equals Early Start plus duration. When an activity has more than one predecessor, its Early Start is the latest of the predecessors' Early Finish dates — you cannot start until the slowest input arrives.
The backward pass runs right to left from the project finish and produces the latest each activity can happen without delaying the project. Late Start equals Late Finish minus duration. When an activity has more than one successor, its Late Finish is the earliest of the successors' Late Start dates.
One practical note before the example: different textbooks number days differently, some starting at day zero and some at day one with a compensating adjustment. The relationships are identical either way. Pick one convention, use it every time you practice, and the arithmetic stops being a source of error. The example below starts the project at day 0.
A worked example
Take this network:
| Activity | Duration | Predecessor |
|---|---|---|
| A | 3 | — |
| B | 5 | A |
| C | 2 | A |
| E | 1 | C |
| D | 4 | B, E |
There are two paths from start to finish:
- A to B to D: 3 + 5 + 4 = 12 days
- A to C to E to D: 3 + 2 + 1 + 4 = 10 days
The critical path is A-B-D at 12 days. That is the answer to "what is the shortest possible project duration" — the longest path and the shortest possible duration are the same number, which sounds like a contradiction until you have said it out loud a few times.
Running both passes gives this:
| Activity | ES | EF | LS | LF | Total float | Free float |
|---|---|---|---|---|---|---|
| A | 0 | 3 | 0 | 3 | 0 | 0 |
| B | 3 | 8 | 3 | 8 | 0 | 0 |
| C | 3 | 5 | 5 | 7 | 2 | 0 |
| E | 5 | 6 | 7 | 8 | 2 | 2 |
| D | 8 | 12 | 8 | 12 | 0 | 0 |
Notice D. It has two predecessors, B finishing at 8 and E finishing at 6, so its Early Start is 8 — the later of the two.
Total float versus free float
These two are the most common source of wrong answers on schedule questions, because candidates learn one, assume the other means the same thing, and then meet a question specifically built to separate them.
Total float is the amount of time an activity can be delayed without delaying the project finish date. Calculate it either way:
- Total float = LS − ES
- Total float = LF − EF
Free float is the amount of time an activity can be delayed without delaying the early start of any successor activity:
- Free float = ES of the successor − EF of this activity
Look at C and E in the table. Both have two days of total float, because the whole A-C-E-D branch has two days of slack relative to the critical path. But C has zero free float: delay C by one day and E's early start moves with it. E has the full two days of free float, because E is the last activity before the merge point at D, and D cannot start before day 8 anyway.
That is the general pattern worth memorizing. When several non-critical activities sit in sequence on the same branch, they share the branch's total float, but the free float usually collects at the activity just before the paths converge. Free float exists only on non-critical activities where paths merge.
So when a question asks how long an activity can slip, read which consequence it is asking about:
- "…without delaying the project" is total float.
- "…without affecting any other activity" or "without delaying its successor" is free float.
Negative float is the third case. If total float comes out negative, the schedule is already behind: the network cannot meet the imposed date without change. It is not an arithmetic mistake and it is not something to ignore — it is the signal that corrective action is required.
When the critical path is too long
The natural follow-up question is what to do when the calculated duration exceeds the date the project has been given. Two schedule compression techniques come up:
Crashing shortens the schedule by adding resources — more people, overtime, extra equipment. Project Management Academy describes crashing as modifying a project's standard progress to speed up the timeline, and its main trade-off is cost: crashing is more likely to increase project costs, while leaving risk broadly where it was.
Fast tracking shortens the schedule by overlapping activities that were planned in sequence. It does not add cost directly, but it increases risk and raises the potential for rework, because work starts before its predecessor is finished and coordination problems follow.
The exam-relevant summary: crashing buys time with money, fast tracking buys time with risk. Neither helps at all unless applied to activities on the critical path — shortening an activity that already has float changes nothing about the project finish date. If an answer option proposes compressing a non-critical activity, it is wrong regardless of how sensible it sounds.
Traps worth rehearsing
- Multiple critical paths. Two paths can tie for longest. Both are critical, both have zero float, and the project is now more fragile, not less, because a delay on either one moves the finish date.
- The path changes. Compress the critical path enough and a different path becomes the longest. Recalculate rather than assuming the original path stays critical.
- A delay inside the float budget. If a non-critical activity slips by less than its total float, the project finish date does not move. The correct answer is often to record the change and continue monitoring, not to escalate.
- Counting the paths. In a network with several branches, list every path explicitly and total each one before deciding. Most wrong answers on these questions come from missing a path, not from bad arithmetic.
How to practice this
Do not read about float. Draw networks and calculate them. Five activities, then eight, then a network with a merge and a parallel branch. Do both passes, fill in total and free float for every activity, and check that the critical path activities came out at zero.
Ten minutes of this a few times a week is enough to make the whole category automatic, and it is a category where automatic is achievable. On exam day, these should be the questions you are pleased to see.