Critical Path

Identifying the critical path is the difference between a level 9–10 project plan and a screenshot of a Gantt chart — it is the one concept the C1-3 interview tests hardest on planning.

Start with a Gantt chart

A Gantt chart shows tasks as horizontal bars on a timeline. The length of each bar = the task's duration. The position of each bar encodes dependencies: a successor task's bar can't start until its predecessor's bar ends. Your GitHub Projects Roadmap View is a Gantt chart — it just doesn't label the critical path for you. See Roadmap View vs Gantt Chart for how they compare.

The critical path — the bottleneck

Think of the critical path as the bottleneck chain: the longest sequence of dependent tasks from the very start of your project to the very end. It sets the minimum possible finish date. If any task on this chain slips by a day, the whole project finishes a day late — there is no buffer anywhere along it.

Finding it by eyeball

Here's a 19-day project with 8 tasks (A–H):

gantt
    dateFormat  D
    axisFormat  Day %d
    tickInterval 1day

    section Critical path
    A  : crit, a, 0, 3d
    B  : crit, b, after a, 4d
    D  : crit, d, after b, 5d
    G  : crit, g, after d, 4d
    H  : crit, h, after g, 3d

    section Off-path (slack)
    C  : c, 0, 5d
    E  : e, after c, 4d
    F  : f, after b, 2d

Trace the chain where bars touch end-to-end with no gap:

A (days 0–3)
B (days 3–7)
D (days 7–12)
G (days 12–16)
H (days 16–19)

Critical path: A → B → D → G → H.

Why C, E, F aren't on it

These tasks have slack — they can slip without delaying the project end date. Task F finishes at day 7, but its successor G doesn't start until day 12. That's a 5-day gap: F has 5 days of slack. You could delay F by up to 5 days and the project still finishes on time.

The rule

Look for the chain where there's zero breathing room between the end of one bar and the start of the next. That's your critical path.

Why it matters at validation

The C1-3 interview rubric requires level 9–10 students to document dependencies and the critical path (C012-Roadmap-vs-Gantt.md). A Roadmap View screenshot with no annotations cannot evidence this — you must add dependency arrows, highlight the critical path, and label slack on non-critical tasks before your interview.

"Trace your critical path" is a Tier 4 interview question. The expected response is to point to your annotated plan and explain: which tasks form the chain, why each dependency exists, what the minimum project duration is, and which tasks have slack. Saying "I think these tasks are the most important ones" is not an answer — the critical path is defined by dependency chains and duration, not importance (C013-Milestones-and-Dependencies.md).

Common mistake: confusing "important tasks" with "critical path tasks." Some important tasks have slack and are not on the critical path. Some critical path tasks are routine — they are critical because of where they sit in the dependency chain, not because they are difficult.

Go deeper — the maths

If you want to calculate critical path the formal way (EST, LST, EFT, LFT, float), watch this: