critical path
The longest chain of dependent work from start to finish; its length is the shortest time the project can take. Any delay on it moves the end date, so it is where attention and extra help pay off.
The critical path is the longest chain of dependent work from the start of a project to its finish. Its length is the shortest time the whole project can take: work can run in parallel elsewhere, but not along this chain. Adding up every task's duration gives the wrong answer, because it ignores everything that runs at the same time.
It is found with two passes over the task network. The forward pass gives each task its earliest start (the latest earliest finish among the tasks it waits for) and its earliest finish (start plus duration). The backward pass starts from the end and gives each task its latest finish (the earliest latest start among the tasks that wait for it) and latest start. Float is latest start minus earliest start: how long a task can slip without moving the end. Tasks with zero float form the critical path.
That is where attention pays off. A delay on the critical path moves the end date day for day; a delay elsewhere is absorbed until its float runs out. Speeding up a task that is not critical saves nothing. Tasks in a row draw on the same float: use it on the first and the next has less. It is room for surprises, not permission to start late.
The path can move. Shorten it and another chain may become the longest; gains on the path carry through only if the next tasks can actually start earlier. And durations are not effort divided by people: a second person shortens a task only by the part of the work that can be split, minus the time spent briefing them.
Example
The schedule of Klasna's physics launch has 17 tasks in working days from Monday 2 November 2026. Classes open on Monday 1 February 2027, so all work must end by day 65 (Friday 29 January).
The forward pass finds this critical path:
22 + 10 + 8 + 15 + 5 + 3 + 5 + 2 = 70 days, ending Friday 5 February: five working days late. The tutor chain everyone worried about (demo lessons, onboarding, launch email) has 17 days of float, so shortening the January ads saves nothing.
Options, recomputed on the network:
- A second reviewer: the review drops from 10 to 7 days (8 splittable days halved to 4, plus 2 days of Vira's final pass, plus 1 day to brief), at an assumed 8,000 UAH. Finish: day 67, still 2 days late.
- A parallel question bank: a freelance author writes it from the draft units from day 22; Vira checks it in 2 days after her review. Finish: day 64, float 1.
- Both: review 22–29, bank 22–30, check 30–32, then the test chain to day 62 (Tuesday 26 January), float 3. This is the plan the sponsor approved.
Common mistakes
- Adding up all durations. Parallel work makes the real minimum much shorter than the sum.
- Speeding up the wrong chain. Effort spent on a task with float doesn't move the end date.
- Treating float as each task's own. It is shared along a chain and is room for surprises, not a later start.
- Assuming the path stays put. Shorten it and another chain may become critical; recompute after every change.
- Expecting more people to cut time in proportion. Only the splittable part shrinks, and briefing costs time.
Learn it in the course
- The critical path and float · A forward pass and a backward pass by hand on eight tasks of the physics launch: the earliest finish, the chain with no room, and how much the other tasks can slip.
- Effort is not duration: when adding people helps · Why ten days of review don't become two with five reviewers: the parts that can't be split, the cost of coordinating, and the waiting no extra person removes.
- Case: the schedule to 1 February · Seventeen tasks, one fixed date. Find the critical path and the float, see that the plan lands a week late, compare cutting, parallel work and an extra reviewer, and write Leo the schedule decision.