Critical path method (CPM) shows up on almost every PMP exam. Candidates lose points here for one reason: they try to eyeball the network diagram instead of running the four-step process PMI tests.
Once you do the four steps in order, every CPM question becomes a 90-second calculation. Here is the walkthrough, the float trap that costs people questions, and four practice problems with full reasoning.
What Critical Path Method Actually Is
CPM finds the longest path through your project network. That longest path is the shortest possible time the project can finish.
Two things matter:
- The critical path itself. A list of activities that, if delayed by one day, push the whole project out by one day.
- Float (also called slack). How long a non-critical activity can slip before it becomes critical.
Activities on the critical path have zero float. That is the rule PMI tests over and over.
The 4-Step CPM Process
Every CPM question follows the same order. Do not skip steps.
| Step | What you calculate | Direction |
|---|---|---|
| 1. Forward pass | Early Start (ES) and Early Finish (EF) | Left to right |
| 2. Identify path durations | Sum the durations of each path through the network | Any direction |
| 3. Backward pass | Late Start (LS) and Late Finish (LF) | Right to left |
| 4. Calculate float | LS minus ES (or LF minus EF) for each activity | Any direction |
The two formulas you must memorize:
- Early Finish = Early Start + Duration
- Float = Late Start - Early Start = Late Finish - Early Finish
That is it. No other math is needed for 95% of CPM questions on the PMP exam.
Forward Pass, Step by Step
The forward pass tells you the earliest each activity can start and finish.
Rules:
- Start with ES = 0 (or 1, depending on the convention. PMI usually uses 0).
- EF = ES + Duration.
- The next activity's ES = the EF of the activity before it.
- If two activities feed into one activity, the next ES is the larger of the two predecessor EFs. (You take the longer path because all predecessors must finish before the next one can start.)
The fourth rule is where most candidates trip. They average the two paths or pick the smaller one. Always take the larger one on the forward pass.
Backward Pass, Step by Step
The backward pass tells you the latest each activity can finish without delaying the project.
Rules:
- Start with the project end. LF of the last activity = its EF.
- LS = LF - Duration.
- The previous activity's LF = the LS of the activity after it.
- If one activity feeds into two activities, the previous LF is the smaller of the two successor LSs.
On the backward pass, you take the smaller value when paths converge. Forward pass = larger. Backward pass = smaller. Memorize that.
Float: The Trap That Costs People Points
Float is the gap between when an activity could start (ES) and when it must start (LS).
Activities on the critical path have float = 0. Activities off the critical path have float > 0.
Two flavors of float that PMI loves to test:
- Total float. How long an activity can slip without delaying the project end date.
- Free float. How long an activity can slip without delaying its successor's early start.
If a question just says "float," assume total float. If it says "free float," do the calculation differently: free float = ES of next activity - EF of current activity.
About 1 in 4 CPM questions on the exam tests free float specifically. If you only know total float, you will miss those.
For more on stem-reading traps, see PMP situational questions: how to read the stem.
4 Worked Practice Questions
Question 1: Find the Critical Path
A project has four paths from Start to End:
- Path A: 5 + 3 + 7 = 15 days
- Path B: 6 + 4 + 8 = 18 days
- Path C: 4 + 9 + 2 = 15 days
- Path D: 7 + 6 = 13 days
What is the critical path duration?
A) 13 days
B) 15 days
C) 18 days
D) 22 days
The critical path is the longest path through the network. Path B is 18 days. Path D is the shortest at 13 days, which is irrelevant.
The trap: candidates pick D because they read "shortest possible project time" and assume that means the smallest path number. The shortest possible project time equals the longest path, because every path must complete.
Answer: C, 18 days.
Question 2: Calculate Total Float
Activity X has these values:
- Early Start: day 5
- Early Finish: day 10
- Late Start: day 8
- Late Finish: day 13
What is the total float of Activity X?
A) 0 days
B) 3 days
C) 5 days
D) 8 days
Total float = LS - ES = 8 - 5 = 3.
You can also calculate it as LF - EF = 13 - 10 = 3. Both methods give the same answer for total float. If they do not match, you made an arithmetic error in your forward or backward pass.
Answer: B, 3 days.
Notice this activity is not on the critical path because its float is greater than zero.
Question 3: Free Float vs Total Float
Activity Y has an Early Finish of day 12. Its only successor, Activity Z, has an Early Start of day 15. Activity Y has a Late Finish of day 18.
What is the free float of Activity Y?
A) 0 days
B) 3 days
C) 6 days
D) Cannot be calculated
Free float = ES of next activity - EF of current activity = 15 - 12 = 3.
The trap: total float here would be LF - EF = 18 - 12 = 6. If you grabbed total float by reflex, you picked C and got it wrong.
Answer: B, 3 days.
The lesson: read for "free" or "total" before you calculate. They are different numbers from the same network.
Question 4: The Schedule Compression Trap
Your project has a critical path of 30 days. The sponsor wants it done in 25 days. You can crash 3 activities:
- Activity A: save 2 days, costs $10,000
- Activity B: save 4 days, costs $30,000
- Activity C: save 5 days, costs $40,000
Activity B is on the critical path. Activities A and C are on a non-critical path.
Which activity should you crash first?
A) Activity A, lowest cost
B) Activity B, on the critical path
C) Activity C, biggest time savings
D) Crash all three to be safe
Crashing only matters on the critical path. Activity A and Activity C are on a non-critical path, so crashing them changes nothing about the project end date.
You will save money on those two activities and your end date will not move. That is wasted budget.
Activity B is the only option. It saves 4 days at $30,000, which gets you from 30 days to 26 days. You still need to find one more day of compression on the critical path with another method (fast-tracking, scope reduction, or another crashable activity not listed).
Answer: B, Activity B.
The trap: candidates pick C because they see "5 days saved" and think bigger savings = better. Only critical-path activities count for compression. This is one of the most-missed CPM questions in PMI Study Hall.
What CPM Questions Actually Test
Every CPM question on the PMP exam falls into one of these buckets:
- Find the critical path (longest path through the network).
- Calculate float for an activity (LS - ES, or free float = ES of next - EF of current).
- Identify the impact of a delay (delay on critical path = project delay; delay on non-critical = float consumed).
- Pick the right compression activity (only critical path activities count; lowest cost per day saved wins ties).
If you can do these four operations, you can answer every CPM question PMI throws at you.
For schedule + cost integration questions, also drill the EVM formulas cheat sheet and the 4 EAC formulas. PMI loves to combine CPM with earned value math in scenario questions.
The One-Sentence Mental Check
Before you answer any CPM question, ask yourself: "Am I working on the longest path, and is this activity on the critical path?"
If the answer is no, the activity has float and a delay does not move the end date. If the answer is yes, every day matters and float is zero.
That single sentence solves the schedule compression trap, the float-confusion trap, and the path-identification trap in one move.
Practice Plan for the Next 7 Days
Day 1: Draw a 5-activity network from scratch and run the forward pass, backward pass, and float for every activity. No shortcuts.
Day 2: Repeat with a 7-activity network that has two converging paths.
Day 3 through 7: Drill 10 CPM questions per day from a question bank. Track which trap caught you (path ID, float type, compression). After 50 questions you will see the same 4 patterns repeating.
CPM is one of the few PMP topics where 7 days of focused practice can move you from 50% accuracy to 90%+. The math is small. The reading discipline is the whole game.
PassCoach.ai is in beta waitlist. First 100 signups get lifetime access for $99. Every CPM question comes with per-option rationales, so when you pick the wrong activity to crash you see exactly which assumption broke down (you ignored the critical path, you confused free and total float, you averaged converging paths instead of taking the larger value), not just which letter was right.
