What is a critical path?
The critical path is the longest chain of dependent tasks through a project: the sequence whose combined duration determines the earliest possible finish date. Every task on it has zero slack, meaning a one-day delay to any of them delays the whole project by a day. Tasks off the critical path have slack: they can slip, up to a point, without moving the end date at all.
The concept comes from the critical path method (CPM), developed in the late 1950s for industrial scheduling, and it remains the single most useful fact you can know about a plan's schedule.
How it is computed#
The critical path is a property of the planning graph, found with two passes over it:
- Forward pass. Walk tasks in dependency order, computing each task's earliest start (the latest finish among its predecessors) and earliest finish.
- Backward pass. Walk in reverse from the project end, computing each task's latest start and finish that would still not delay the project.
A task's slack (or float) is the gap between its earliest and latest start. The critical path is the chain of tasks where that gap is zero.
| Term | Meaning |
|---|---|
| Earliest start | The soonest a task can begin, given its predecessors |
| Slack / float | How far a task can slip without moving the project end |
| Critical task | A task with zero slack |
| Critical path | The end-to-end chain of critical tasks (the longest path) |
Why it matters#
The critical path converts "everything is important" into an actionable asymmetry. Accelerating a critical task shortens the project; accelerating a non-critical one does nothing to the end date. Watching the critical path is managing the schedule; watching everything else is managing busywork. The same logic prices delays: a two-day slip on a task with five days of slack costs nothing, while a two-hour slip on a critical task costs exactly two hours of project.
The classical blind spot#
Textbook CPM treats task durations as fixed numbers, so it returns exactly one critical path. Real durations are uncertain, and under uncertainty the critical path is not a fixed object: different futures have different longest chains, and a chain with "two days of slack" on paper is one bad week from taking over. The honest, modern treatment computes the critical path per simulated future and reports how often each chain decides the finish, which is the subject of the near-critical path definition and the full essay.
In Topolog, the critical path is computed continuously from the live plan (no separate network diagram to maintain) and shown in its own tab, alongside the probabilistic view: which chains decide your finish date, and how often. The critical path docs cover the product surface.