WhenMathCritical Path Basics: Why Some Delays Slip the Deadline
On a multi-phase plan, a delay in one phase may push the deadline back by that amount, or have no effect at all, depending on whether that phase has schedule slack.
When a project has multiple phases with dependencies between them (some phases can run in parallel, others must wait for an earlier phase to finish), not every phase's timing affects the final completion date equally. The critical path is the specific sequence of dependent phases with zero slack, meaning any delay in one of those phases delays the final deadline by the same amount. A phase not on the critical path has some slack (float): it can run late, up to a point, without moving the final deadline at all.
How slack is computed
For each phase, a forward pass through the dependency graph computes the earliest it could start and finish given its predecessors, and a backward pass from the final deadline computes the latest it could start and finish without delaying that deadline. The difference between those two windows for a given phase is its slack. A phase with zero slack is on the critical path, and a phase with positive slack has that much room to run late before it starts affecting the deadline.
Why this matters more than a simple total-duration sum
Simply adding up every phase's duration overstates the real minimum project length whenever any phases can run in parallel, and it gives no information about which specific phase to watch most closely for delay risk. Knowing the actual critical path tells you exactly which phases have zero margin for error and which ones can absorb some slippage without any consequence to the final date.
What changes when a critical-path phase is delayed vs. accelerated
Delaying a critical-path phase pushes the final deadline back by the same amount, with no absorption. Accelerating a critical-path phase can pull the deadline forward, but only up to the point where a different phase (previously non-critical) becomes the new critical path with its own zero slack. WhenMath's Phase Dependency Planner and Schedule Slack Calculator both compute this directly from a stated dependency graph rather than requiring a manual slack calculation.
Key takeaway. Only phases on the critical path (zero slack) directly delay the final deadline when they run late. A phase with slack can absorb some delay with no effect on the deadline, up to the size of its slack.
Frequently asked
- Can a project have more than one critical path?
- Yes, if two or more dependency chains happen to have exactly the same total duration to the final deadline, they are all critical simultaneously, and a delay in any one of them delays the deadline.
- Does adding more people to a delayed phase always help?
- Only if that phase is actually on the critical path. Speeding up a phase with slack has no effect on the final deadline at all, which is why identifying the critical path before reallocating effort matters.
- How does this relate to a deadline buffer?
- A buffer (covered in its own resource above) is deliberately reserved slack added to protect a deadline, while critical-path slack is the naturally occurring slack that already exists in a dependency graph before any buffer is added on top of it.
Related engines
- Multi-Phase Deadline Planner -- Model sequential and parallel phases and find the finish date and critical path.
- Phase Dependency Planner -- Model phases and dependencies as a graph and find the finish date and critical path.
- Schedule Slack Calculator -- Calculate float: the difference between available time and required time.
Last updated 2026-09-04