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6.4 Critical Path and Schedule Calculations

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CAPM Certified Associate in Project Management Exam

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1 Chapter 1: Introduction & CAPM Exam Overview

1.1 About the CAPM Exam 1.2 PMBOK 7th Edition Overview 1.3 Exam Content Outline (ECO) 1.4 CAPM vs. PMP: Understanding the Differences

2 Chapter 2: Project Life Cycles and Processes (Domain 1, Tasks 1-2)

2.1 Projects, Programs, and Portfolios 2.2 Project Life Cycle Phases 2.3 The Five Process Groups 2.4 The Ten Knowledge Areas

3 Chapter 3: Project Management Planning (Domain 1, Task 2)

3.1 The Project Management Plan 3.2 Scope Management and the WBS 3.3 Schedule Management 3.4 Cost Management and Earned Value 3.5 Quality Management

4 Chapter 4: Project Roles, Responsibilities, and Ethics (Domain 1, Tasks 3-4)

4.1 Project Roles and Responsibilities 4.2 Leadership and Emotional Intelligence 4.3 Risk Management Fundamentals 4.4 PMI Code of Ethics and Professional Conduct 4.5 Problem-Solving Tools and Techniques

5 Chapter 5: Resource, Communication, and Stakeholder Management (Domain 1, Tasks 2-3)

5.1 Resource Management 5.2 Communications Management 5.3 Stakeholder Management 5.4 Procurement Management 5.5 Issues, Risks, Assumptions, and Constraints

6 Chapter 6: Predictive, Plan-Based Methodologies (Domain 2)

6.1 When to Use a Predictive Approach 6.2 WBS, Work Packages, and Activity Definition 6.3 Predictive Project Controls and Artifacts 6.4 Critical Path and Schedule Calculations

7 Chapter 7: Agile Frameworks and Methodologies (Domain 3, Tasks 1-3)

7.1 When to Use an Adaptive (Agile) Approach 7.2 The Scrum Framework 7.3 Kanban, XP, and SAFe 7.4 Agile Planning, Estimation, and Metrics 7.5 Agile Project Controls and Artifacts

8 Chapter 8: Business Analysis Roles and Stakeholder Communication (Domain 4, Tasks 1-2)

8.1 Business Analysis Roles and Responsibilities 8.2 Stakeholder Communication in Business Analysis 8.3 Business Case and Needs Assessment

9 Chapter 9: Requirements Gathering and Product Roadmaps (Domain 4, Tasks 3-4)

9.1 Requirements Gathering Approaches 9.2 Requirements Traceability Matrix 9.3 Product Roadmaps

10 Chapter 10: BA Methodologies and Requirements Validation (Domain 4, Tasks 5-6)

10.1 Business Analysis in Predictive and Agile Approaches 10.2 Acceptance Criteria and Requirements Validation 10.3 Business Analysis Tools and Techniques Summary

6.4 Critical Path and Schedule Calculations

Key Takeaways Explain This Topic AI

The forward pass calculates Early Start (ES) and Early Finish (EF) left to right; EF = ES + Duration

The backward pass calculates Late Start (LS) and Late Finish (LF) right to left; LS = LF - Duration

Total float = LS - ES = LF - EF; the critical path is the longest path and its activities have zero total float

Free float is how long an activity can slip without delaying the EARLY START of any successor (a different idea from total float)

Crash the critical-path activity with the lowest cost per time unit first; fast-tracking overlaps activities and adds risk

Last updated: June 2026

Network Diagram Basics

A project schedule network diagram shows the logical dependencies between activities. The most common method, Precedence Diagramming Method (PDM) , draws each activity as a node and uses four relationship types: Finish-to-Start (FS) is by far the most common, plus Start-to-Start (SS), Finish-to-Finish (FF), and the rare Start-to-Finish (SF). Each node carries the scheduling values: +------+----------+------+

  • | ES | Duration | EF |
  • +------+----------+------+
  • | Activity |
  • +------+----------+------+
  • | LS | Float | LF |
  • +------+----------+------+
  • Term Abbrev. Definition
  • Early Start ES Earliest an activity can start
  • Early Finish EF Earliest an activity can finish
  • Late Start LS Latest it can start without delaying the project
  • Late Finish LF Latest it can finish without delaying the project
  • Duration D Time to complete the activity

The critical path is the longest duration path through the network; it sets the shortest possible project duration. Its activities have zero total float , so any delay to them delays the whole project.

Forward Pass — Compute ES and EF

Move left to right . EF = ES + Duration. The first activity starts at ES = 0 (this guide uses the zero convention; some texts start at 1). When an activity has multiple predecessors , its ES = MAX of all predecessor EFs — it cannot start until every predecessor finishes.

Network: A(3) -> B(5) and C(4); B and C -> D(2).

  • A: ES = 0, EF = 0 + 3 = 3
  • B (after A): ES = 3, EF = 3 + 5 = 8
  • C (after A): ES = 3, EF = 3 + 4 = 7
  • D (after B and C): ES = MAX(8, 7) = 8 , EF = 8 + 2 = 10

Project duration = 10 (the EF of the last activity).

Backward Pass — Compute LF and LS

Move right to left . LS = LF - Duration. The last activity's LF equals the project duration. When an activity has multiple successors , its LF = MIN of all successor LSs.

  • D: LF = 10, LS = 10 - 2 = 8
  • B: LF = 8 (LS of D), LS = 8 - 5 = 3
  • C: LF = 8 (LS of D), LS = 8 - 4 = 4
  • A: LF = MIN(3, 4) = 3 , LS = 3 - 3 = 0

Calculating Float

Total float = LS - ES = LF - EF. It is how long an activity can slip without delaying the project finish. Free float is different: how long an activity can slip without delaying the early start of any successor . On the exam, unqualified "float" means total float.

Activity ES EF LS LF Total float Critical?

  • A 0 3 0 3 0 Yes
  • B 3 8 3 8 0 Yes
  • C 3 7 4 8 1 No
  • D 8 10 8 10 0 Yes

Critical path: A -> B -> D (the zero-float chain; length 3 + 5 + 2 = 10). Activity C has 1 day of float, so it can slip one day without harming the finish date.

Leads and Lags

  • Concept Meaning Effect
  • Lead Successor starts before the predecessor finishes Compresses schedule (negative lag), e.g., FS - 2 days
  • Lag Mandatory wait after the predecessor before the successor starts Extends schedule, e.g., FS + 3 days

Lag example: after pouring concrete you must wait 3 days for curing before building walls — FS + 3. Lead example: you begin editing a document 2 days before drafting fully finishes — FS - 2.

Schedule Compression

Two techniques shorten the schedule; both apply only to the critical path , because shortening a non-critical activity does nothing for the finish date.

Crashing

Add resources/cost to shorten duration. Always crash the critical-path activity with the lowest cost per time unit first, then recompute — the critical path can shift .

  • Activity Normal Crash Normal cost Crash cost Crash cost/day
  • A 10 d 8 d $5,000 $7,000 $1,000/day
  • B 8 d 6 d $4,000 $7,000 $1,500/day
  • C 6 d 5 d $3,000 $4,500 $1,500/day

If A and B are on the critical path, crash A first ($1,000/day beats $1,500/day). Crashing increases cost and may not preserve quality, but it does not add scope risk.

Fast-tracking

Perform activities (or phases) in parallel that were planned sequentially — e.g., start design of module 2 before module 1 design is fully done. Fast-tracking adds no direct cost but increases risk and rework .

Technique Adds cost? Adds risk?

  • Crashing Yes Low (no rework)
  • Fast-tracking No Yes (rework/risk)

Exam tips: (1) Never crash a non-critical activity — it cannot shorten the project. (2) After any compression, recalculate the network; a previously near-critical path may become the critical path. (3) If two paths tie for longest, the project has two critical paths , and any delay on either delays the project.