PMP Critical Path Method: Free Float Calculation Practice (2026)

The Critical Path Method (CPM) is the backbone of PMP schedule management. Exam questions test whether you can build a network, identify the longest path, and compute float under time pressure. Here is the method.

Step 1: Build the Network

List every activity, its duration and its predecessors. Draw nodes (activities) connected by arrows (dependencies). Common conventions:

• Activity-on-Node (AON): the PMBOK default — each node is an activity, arrows show dependencies.
• Activity-on-Arrow (AOA): older; activities are arrows, nodes are events. Rare in the PMP exam now.

Step 2: Forward Pass — Early Dates

Compute the Earliest Start (ES) and Earliest Finish (EF) for each activity, left to right:

• ES(activity) = max of EF of all predecessors (0 for the first).
• EF = ES + duration.

The largest EF at the end of the network is the minimum project duration.

Step 3: Backward Pass — Late Dates

Compute Latest Finish (LF) and Latest Start (LS), right to left:

• LF(last activity) = project duration (the EF from the forward pass).
• LF(activity) = min of LS of all successors.
• LS = LF − duration.

Step 4: Calculate Float

Total Float (TF) = LS − ES = LF − EF. The amount of time an activity can slip without delaying the project.

Free Float (FF) = ES(next) − EF(this) — the slack before delaying the next activity.

Project Float = contractual end date − calculated project end (when a deadline is imposed).

Step 5: Identify the Critical Path

The path whose total float = 0 at every activity is the critical path. Equivalently, it is the longest-duration path. If two paths tie, both are critical.

Worked Example

Activities: A(5) → B(4) → D(3); A → C(7) → D. (D depends on both B and C.)

Forward pass:

• A: ES 0, EF 5
• B: ES 5, EF 9
• C: ES 5, EF 12
• D: ES = max(EF B, EF C) = max(9, 12) = 12; EF = 15

Project duration = 15. The critical path is A → C → D (12 is the controlling value at D).

Backward pass:

• D: LF 15, LS 12
• B: LF = LS D = 12, LS = 12 − 4 = 8
• C: LF = LS D = 12, LS = 12 − 7 = 5
• A: LF = min(LS B, LS C) = min(8, 5) = 5, LS = 5 − 5 = 0

Floats:

• A: TF = 0 (critical)
• B: TF = LS − ES = 8 − 5 = 3
• C: TF = 0 (critical)
• D: TF = 0 (critical)

Path A → C → D = 15 (critical); path A → B → D = 12 with 3 days of slack on B.

PMP Exam Patterns

• “Which activity can slip without delaying the project?” → one with float (non-critical).
• “Which path is critical?” → the longest path; or the one with zero float at every activity.
• “If activity X is delayed by N days, is the project delayed?” → compare delay to X’s total float. If delay ≤ float, no; if delay > float, yes, by the overrun.
• Near-critical path: a path whose float is very small — a risk, because a small slip makes it critical.

Common Mistakes

• Forgetting to take the max of predecessor EFs in the forward pass.
• Forgetting to take the min of successor LSs in the backward pass.
• Adding an activity’s duration twice (use ES + duration = EF, then ES of next = EF of previous).
• Assuming a path with the most activities is critical — it is the path with the longest total duration.

Fast-Check Heuristics

• Critical path activities have ES = LS and EF = LF (float = 0).
• Total float = free float only when the activity is on the critical chain feeding the next critical activity.
• Any activity on the critical path that is delayed delays the project one-for-one.

Master the forward/backward pass, the float formulas, and the “delay vs float” comparison, and the schedule questions on the PMP exam become pure routine.