What is the Critical Path?
The critical path (English: Critical Path) is the longest chain of time-dependent activities in a project. It determines the minimum project duration -- the project cannot be completed faster than the critical path dictates.
What's special about activities on the critical path: They have no buffer time. If a critical activity takes three days longer than planned, the project end date shifts by exactly three days. Non-critical activities, on the other hand, have a buffer -- they can be delayed within this buffer without jeopardizing the project end date.
For project managers, the critical path is therefore one of the most important planning tools: It shows where delays directly threaten the project and where there is leeway. In combination with a Gantt chart, the project structure becomes visually tangible.
The Critical Path Method (CPM) was developed in 1957 by the US companies DuPont and Remington Rand for planning plant maintenance projects. Almost simultaneously, the PERT method (Program Evaluation and Review Technique) was created for the US Navy's Polaris missile program. Both methods form the basis of modern network planning and are still part of the PMBOK Guide (PMI) and DIN 69900 today.
The Critical Path Method (CPM) Explained
CPM is based on a network diagram that maps all activities of a project, their duration, and their dependencies. From this network diagram, the earliest and latest times for each activity are determined through forward and backward pass calculations.
The central terms of CPM are:
- ES (Earliest Start): The earliest possible start date of an activity
- EF (Earliest Finish): The earliest possible finish = ES + Duration
- LS (Latest Start): The latest start date without jeopardizing the project end date
- LF (Latest Finish): The latest finish = LS + Duration
- TF (Total Float): The maximum delay without impact on the project end date = LS - ES
- FF (Free Float): The maximum delay without impact on the direct successor
Core Rule: All activities whose total float is zero (TF = 0) lie on the critical path. They must not be delayed.
The Critical Path — Visualized
The longest path through the network determines the minimum project duration. Delays on this path delay the entire project.
The Critical Path (red) determines the minimum duration of 10 weeks. Non-critical tasks (gray) have float time.
Calculating the Critical Path: Step-by-Step
Create Activity List
List all project activities with their duration and their dependencies (predecessors). Each activity must have at least one predecessor, except for the start activity.
Forward Pass
Calculate for each activity the earliest start (ES) and the earliest finish (EF), starting with the first activity with ES = 0. The formula: EF = ES + Duration. If an activity has multiple predecessors, its ES is equal to the maximum of all EF values of the predecessors.
Backward Pass
Calculate for each activity the latest finish (LF) and the latest start (LS), starting with the last activity. The LF of the last activity corresponds to its EF from the forward pass. The formula: LS = LF - Duration. If an activity has multiple successors, its LF is equal to the minimum of all LS values of the successors.
Calculate Float and Identify the Critical Path
Calculate the Total Float: TF = LS - ES (or equivalently: LF - EF). All activities with TF = 0 lie on the critical path. Connect these activities -- they form the longest path through the network diagram.
Practical Example: Website Relaunch
A company plans a website relaunch with six activities. The goal is a complete project plan with an identified critical path and defined milestones.
Activity List
| Activity | Description | Duration (Days) | Predecessor |
|---|---|---|---|
| A | Requirements Analysis | 5 | -- |
| B | UX Design | 8 | A |
| C | Content Creation | 6 | A |
| D | Frontend Development | 10 | B |
| E | Backend Development | 12 | B |
| F | Testing & Go-Live | 4 | C, D, E |
Forward Pass
B: ES=5, EF=5+8=13
C: ES=5, EF=5+6=11
D: ES=13, EF=13+10=23
E: ES=13, EF=13+12=25
F: ES=max(11,23,25)=25, EF=25+4=29 Project duration: 29 days. F waits for the latest predecessor (E, Day 25).
Backward Pass
E: LF=25, LS=25-12=13
D: LF=25, LS=25-10=15
C: LF=25, LS=25-6=19
B: LF=min(15,13)=13, LS=13-8=5
A: LF=min(5,19)=5, LS=5-5=0 B has two successors (D and E). The LF of B is the minimum of the LS values of D (15) and E (13) = 13.
Float and Critical Path
| Activity | Duration | ES | EF | LS | LF | TF | Critical? |
|---|---|---|---|---|---|---|---|
| A | 5 | 0 | 5 | 0 | 5 | 0 | Yes |
| B | 8 | 5 | 13 | 5 | 13 | 0 | Yes |
| C | 6 | 5 | 11 | 19 | 25 | 14 | No |
| D | 10 | 13 | 23 | 15 | 25 | 2 | No |
| E | 12 | 13 | 25 | 13 | 25 | 0 | Yes |
| F | 4 | 25 | 29 | 25 | 29 | 0 | Yes |
This path has a total duration of 5 + 8 + 12 + 4 = 29 days. Any delay on this path extends the project. Activity C has 14 days of float -- it could not start until day 19 without jeopardizing the go-live date. Activity D has 2 days of float and is therefore "near-critical".
Advantages and Limitations of the Method
Advantages of CPM
- Focus on the Essentials: CPM shows which activities are critical for project success. Resources and management attention can be focused specifically on critical activities.
- Realistic Scheduling: The minimum project duration is determined mathematically, not estimated. This prevents unrealistically optimistic schedules.
- Float Management: Non-critical activities have measurable float. This can be used consciously -- e.g., for resource leveling or parallel project work.
- Scenario Analysis: "What happens if activity X takes three days longer?" -- with CPM, the impact of any change can be calculated immediately.
Limitations of CPM
- Rigid Duration Estimates: Classic CPM works with fixed duration values. In reality, durations fluctuate. The PERT method addresses this with optimistic, most likely, and pessimistic estimates.
- No resource consideration: CPM does not consider whether sufficient personnel or capacity is available. Two parallel tasks might require the same person.
- Complexity in large projects: For projects with hundreds of tasks, manual calculation becomes impractical. Software tools are then indispensable.
- Less suitable for agile projects: In agile methods like Scrum, scope and priorities change continuously. The critical path then constantly shifts.
Critical Path in Practice: Tools and Software
Various tools are available for calculating the critical path. The choice depends on project size and complexity:
- Excel / Google Sheets: For small projects with up to 20 tasks, forward and backward pass calculations can be mapped in spreadsheets. Beyond a certain complexity, this becomes error-prone.
- Microsoft Project: The classic for CPM calculations. Automatically calculates the critical path and displays it in red in the Gantt chart. Requires a license and training time.
- Specialized PM software: Tools like Primavera P6 (for large projects), Smartsheet, or Monday.com offer CPM features to varying depths.
- AI-powered tools: Modern solutions like PathHub AI automatically calculate dependencies and phase durations based on the project description -- without manual network diagram creation.
How PathHub AI Considers the Critical Path
PathHub AI generates project plans with clearly defined phases, tasks, and dependencies. In doing so, the AI automatically considers the logical sequence of tasks and estimates realistic durations.
- Automatic phase planning: The AI recognizes which tasks can run sequentially and which can run in parallel -- the foundation for the critical path.
- Phase duration and dependencies: Each phase receives a realistic time estimate. Tasks within a phase run in parallel, phases build upon each other.
- Timeframe visualization: The total project duration results from the sum of the phase durations -- just as the sum of the critical tasks determines the critical path.
- Customizable plans: If durations or dependencies change, you can adjust the plan. PathHub AI helps you assess the impact on the overall duration.