What makes a path critical?
A path is critical when it controls the project’s earliest finish under the schedule model. In a simple finish-to-start network with no extra constraints, it is the longest-duration path. PMI’s scheduling guidance describes this relationship and the need to watch paths that may become critical.
The word longest refers to duration, not the number of activities. A path with three long tasks can control completion while a path with six short tasks does not. Don’t choose the line that looks busiest on the diagram.
Resources, imposed dates, calendars, lags and other constraints can change the analysis. Start with the conditions stated in the question.
How do I calculate a simple critical path?
Add activity durations along each valid dependency path, then compare the totals. In this network, A takes 2 days and splits into B at 5 days or C at 3 days. Both must finish before D, which takes 4 days.
Path A → B → D takes 2 + 5 + 4 = 11 days. Path A → C → D takes 2 + 3 + 4 = 9 days. The B path controls completion because D must wait for both branches.
A shorter branch cannot let a merge activity start early while the longer branch is unfinished. This is a frequent source of mistakes when learners add durations without tracing dependencies.
Scroll sideways to see every column.
| Path | Duration | Result |
|---|---|---|
| A → B → D | 11 days | Controls earliest finish |
| A → C → D | 9 days | Two days shorter |
A finishes before B and C start. Both B and C must finish before D starts.
How do early and late dates give total float?
A forward pass gives early dates, a backward pass gives late dates, and their difference gives total float. Using elapsed-day notation starting at 0, A runs from 0 to 2; B from 2 to 7; C from 2 to 5; and D from 7 to 11.
Working backward from day 11, D must start at 7. B must finish at 7 and start at 2. C can finish at 7 and start at 4. Its total float is 4 − 2 = 2 days, or 7 − 5 = 2 days.
Use one date-counting convention throughout. Mixing elapsed day 0 with inclusive day 1 notation creates off-by-one errors even when you understand the network.
- 01Forward passUse the latest predecessor finish
- 02Backward passUse the earliest successor start
- 03SubtractLate date minus matching early date
What is the difference between total float and free float?
Total float is the delay available without delaying the project finish or violating a schedule constraint; free float is the delay available without delaying a successor’s early start. They are not always equal.
In the simple example, C can finish two days later without moving D’s early start, so it has two days of free float as well as two days of total float. Other networks can give an activity total float that is shared with later work, while its immediate successor has no spare early-start time.
Don’t add every activity’s total float as if it were an independent reserve. Delaying one task can use the flexibility of a path and leave less for another task.
How do I use critical-path results in a PMP decision?
Use critical-path results to identify which delay affects completion and which response might change that result. Shortening a noncritical activity may not shorten the project at all.
Crashing adds resources to shorten suitable work and often increases cost. Fast tracking overlaps work that was planned in sequence and can increase rework risk. Check feasibility and authority rather than treating either technique as a guaranteed fix. PMI’s scheduling standard discusses these tradeoffs.
PMP Exam Coach’s critical-path tools are designed for hands-on dependency practice. Combine them with earned-value interpretation to distinguish work-value signals from finish-date analysis.
