The gates open at seven. The bulbs are still going up, the carousel organ is being tuned, and someone is halfway up the Ferris wheel with an inspection clipboard. Every crew is busy. Only one chain of work controls when the carnival can open.
That is the useful idea behind the critical path method: a project is not delayed by every late activity. It is delayed when work on a critical route pushes the earliest possible finish.
Start with the network, not the spectacle
The carnival schedule uses seven activities and simple finish-to-start relationships. Raising the entrance arch comes first. Three branches then prepare the midway, the carousel parade, and the Ferris wheel. All three must finish before the final safety walk.
The opening plan has three complete routes:
- A-B-E-G: 2 + 4 + 3 + 2 = 11 days
- A-C-F-G: 2 + 3 + 2 + 2 = 9 days
- A-D-G: 2 + 5 + 2 = 9 days
The 11-day midway route is the critical path because it is the longest route through the network. The project cannot finish sooner than its longest required chain.
Forward pass: find the earliest dates
A forward pass moves from the start of the network toward the finish. For each activity:
- Early Start (ES) is the greatest Early Finish among its immediate predecessors. An activity with no predecessor starts at day 0 in this example.
- Early Finish (EF) = ES + duration.
When several branches merge, the next activity must wait for the latest predecessor. The final safety walk cannot begin merely because the Ferris-wheel route is ready; it must wait until the midway and carousel routes are ready too. The largest terminal EF gives the project duration.
Backward pass: protect the opening date
A backward pass starts at the project finish and moves toward the beginning. For each activity:
- Late Finish (LF) is the smallest Late Start among its immediate successors. A final activity takes the project duration as its LF.
- Late Start (LS) = LF - duration.
These late dates show how far an activity can move without changing the current opening date. They are not a suggestion to wait; they are boundaries created by the network.
Total float: measure the room to move
Total Float = LS - ES, which is also LF - EF in this schedule.
Under the opening plan, the activities unique to the two 9-day routes each have 2 days of total float. That means the Ferris-wheel inspection can grow from 5 to 7 days before its route ties the 11-day midway route. At 8 days, the Ferris-wheel route becomes the only critical route and moves opening night to day 12.
Critical activities normally have zero total float in this unconstrained example. If two complete routes tie for the longest duration, both are critical. Shortening only one of them will not shorten the project because the other still controls the finish.
The critical path can move
Criticality describes the current schedule model, not a permanent label attached to an activity. Actual progress, new estimates, changed relationships, or approved schedule compression can create a different critical path. Near-critical routes deserve attention because a small change can make them critical.
If the opening date must move earlier, analyze activities on every current critical path. Crashing can shorten durations by adding resources at additional cost. Fast tracking overlaps work that was planned in sequence and can increase risk or rework. Neither technique is a magic instruction to work faster; each requires a deliberate tradeoff.
What this calculator assumes
The lab below keeps the teaching model intentionally small. It uses finish-to-start relationships, no leads or lags, one shared work calendar, no date constraints, and no resource limitations. Real schedules can produce more complex results, including critical paths driven by constraints or resources.
Use the presets first. Then move one duration at a time. Watch the route totals, project duration, ES, EF, LS, LF, and total float respond together.
Sources and exam note
The definitions and calculation sequence in this guide are supported by PMI's critical path calculation walkthrough and time-management terminology. PMI's schedule-compression discussion explains crashing and fast tracking. Vital Few Prep is an independent study resource with no affiliation to the Project Management Institute. This guide uses original educational material and makes no promise about any particular exam form.