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Critical path method

Basics Schedule Management Reviewed 23 Oct 2026 2 min read

The critical path method finds the shortest time in which a project can be completed and the activities that control that time.

Each activity has a duration and a list of activities it depends on. Drawn as a network, a forward pass from the start gives each activity's earliest start and finish: an activity can start only when all its predecessors have finished. The latest finish of the whole network is the project duration. A backward pass from the end gives each activity's latest start and finish without delaying completion.

Diagram: Indiacon original, not to scale.

Total float is the difference between latest and earliest start. Activities with zero total float form the critical path: delay any of them and the project end moves. Non-critical activities have float that can absorb some delay or be used to smooth resource demand.

CPM assumes fixed durations. PERT adds uncertainty using three time estimates. Real schedules also need calendars, resource limits and constraints, and must be updated as work progresses. Try our CPM calculator.

Tip

Do the forward pass for all activities before starting the backward pass.

Key formulas
  • ES = max(EF of predecessors); EF = ES + duration
  • LF = min(LS of successors); LS = LF − duration
  • Total float TF = LS − ES = LF − EF
Common mistake

Taking the minimum, not the maximum, of predecessor finishes in the forward pass.

Solved example

Problem. Activities: A (3 d), B (4 d) after A, C (2 d) after A, D (5 d) after B and C. Find duration and critical path.

  1. A: 0–3. B: 3–7. C: 3–5. D starts at max(7, 5) = 7, ends 12.
  2. Backward: D LS 7. B LF 7, LS 3. C LF 7, LS 5. A LF = min(3, 5) = 3.
  3. C has float 2; A, B, D have zero float.

Answer. 12 days; critical path A–B–D

Quick quiz

1What defines a critical activity?

Zero total float.

2What does the forward pass give?

Earliest start and finish times.

3If a non-critical activity slips by less than its float, what happens to the end date?

Nothing.

Code note
  • DIN 69900 (Germany): Project management: network techniques.
  • PMI PMBOK Guide / ANSI standard for project management (USA): Framework of project management principles and practices.

Cited by number and clause only. We do not reproduce clause text, tables or figures (BIS Act 2016, s.10(5) and s.11). Check the current edition and amendments before use.

References and further reading

Standard texts, listed in no order of merit. We do not copy text, figures, tables or solved problems from any book; our explanations and examples are original.

  • B. C. Punmia, K. K. Khandelwal, Project Planning and Control with PERT and CPM, Laxmi Publications, latest edition.
  • J. W. Hinze, Construction Planning and Scheduling, Pearson, latest edition.

Free and official sources

All references for this subject →

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