Everything You Need To Know About CPM: The Critical Path Method With Examples

CPM or the Critical Path Method is an algorithm used in project management that is used to schedule project activities. The critical path refers to the longest stretch of the activities, and a measure of them from start to finish. 

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What is the Critical Path Method (CPM)?

A strategy for surveying plan adaptability and distinguishing undertakings fundamental for project culmination is the critical path method (CPM). In the project, the executives, the basic way is the longest succession of undertakings that should be done on time for the task to be done. If crucial tasks are postponed, the project will also be delayed.

CPM Key Elements

The elements of CPM in project management are as follows: 

Earliest Start Time (ES)

The initial stage in the project is when an activity can be begun. You cannot make this decision without initially understanding whether you have any task dependencies.

Latest Start Time (LS)

The very last second when a task can be started without affecting the timeline for your project.

Earliest Finish Time (EF)

The earliest a task can be finished is determined by its duration and earliest start time.

Latest Finish Time (LF)

The latest that a task can be finished is calculated using its duration and latest start time.


The concept of "float" refers to how long an activity can be postponed without affecting its task order or the project timeline. The critical path tasks have no float since they cannot be delayed.

Why Use the Critical Path Method?

CPM can advise sage on setting priorities, distributing resources, and scheduling projects.

There are various reasons to use this method, including the ones listed below:

Improves Future Planning

Improves future planning by utilising CPM to compare expectations with actual progress. Future undertaking thoughts can be affected by the information accumulated from progressing projects.

Facilitates More Effective Resource Management

It lets project managers prioritise tasks, giving them a better understanding of how and where to deploy resources.

Helps Avoid Bottlenecks

Project bottlenecks can cost precious time. By outlining project dependencies using a network diagram, you can more accurately decide which tasks can and cannot be finished in parallel. After that, you can adjust your schedule accordingly.

With the help of CPM, we’ll be able to create a model that enables you to determine the following: 

  • Tasks required to complete the project
  • Dependencies between tasks
  • The duration required to complete an activity

Now, before we can get started with CPM or Critical Path Method, we’ll have to understand two major concepts which are Events and Activities. To help understand them better, let’s have a look at the network diagram (which is also the output) of the process. 

example cpm

This output represents some of the most important parts of the process: Events and Activities.


Events are represented by a circle and will occur at the start and end of an activity. Event 1 is the tail event and Event 2 is the head event. In the case of our example, the events are 1, 2,3,4, 5, and 6. Taking into consideration, nodes 1 and 2, and the connection between them, 1 will be referred to as the tail event, and 2 will be referred to as the head event. 

Similarly, for 2 and 3, 2 is the tail event, and 3 is the head event. 

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Activities represent action and consumption of resources like time, money, and energy required to complete the project. In the case of our example, A, B, C, D, E, and F represent the activities taking place between their respective events. 

Dummy Activity

A dummy activity represents a relationship between two events. In the case of the example below us, the dotted line represents a relationship between nodes 4 and 3.
The activity between these nodes will not have any value. 

dummy act

Other rules to consider

  • The network should have a unique starting and ending node. In the case of our example, event 1 represents a unique starting point and 6 represents the unique completion node
  • No activity can be represented by more than a single arc (the line with an arrow connecting the events) in the network
  • No two activities can have the same starting and ending node. 

Now, let’s talk about the process of the Critical Path Method with an example. 

The Critical Path Method

The objective of the question below is to determine the critical path, based on the information available, like activity, immediate predecessor, and duration (which in this case, we’ll take as months)

question cpm

First, let’s analyze the activities and their immediate predecessors. 

Activities A, B, and C don’t have any immediate predecessors. This means that each of them will have individual arcs connecting to them. First, we’ll draw nodes 1 (which is the starting point) and 2. We’ll add the activity on the arc, along with the duration. 


We’ll have to also keep in mind that A acts as the immediate predecessor for both nodes E and F. Similarly, let’s draw the arcs for nodes B and C. 


Before we can draw the nodes for activity D, a quick look at the table will tell us that it is preceded by activity B and that a combination of activities C and D act as immediate predecessors for activities H and J. This means that both activities C and D have to connect at some point. That’s why we’ll be drawing an arc from events 3 and 4. 


So now, we’ve completed activities A, B, C, and D of the critical path method. Next, let’s take a look at activity E. 

Activity E is preceded by activity A and acts as the immediate predecessor for activity J. Since this is an independent activity, we’ll be able to draw an arc like this.


If we have a look at activity F, it’s preceded by activity A, and a combination of F, G, and H act as immediate predecessors for the activities K and L. So let’s wait before we take it up. Instead, let’s shift our attention to activity G. It’s preceded by B. So, we’ll draw it like so.

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Now, let’s take a look at activity H. It is preceded by both C and D and will act as the immediate predecessor for K and L, along with F and G. So, we can connect node 4 to 6. 

activity h

Now that we’ve done that, let’s go back to activity F.  Now that we know where activities G and H connect to, we can combine nodes 2 and 6, fulfilling the conditions required for activities K and L.

activity f

Following this, we have an activity I. The activity I is preceded by activities C and D. It also acts as an immediate predecessor to activity M. Since it’s an independent activity, we can draw it like so. 

activity i

Next, let’s take a look at activity J. Activity J is preceded by activity E. We can also see that a combination of J and K will act as an immediate predecessor for activity N. We can then draw an arc like this. 

activity j

Let’s go on to activity K. Here we can see that K is preceded by F, G, and H. It also acts as an immediate predecessor to activity N. So, we’ll connect nodes 6 to 8. 

activity k

Next, let’s continue with activity L. The table now shows that L, M, and N don’t act as immediate predecessors for any other activity. Hence it can be assumed that it’ll connect to the final node. 

L is preceded by activities by F, G, and H. The arc can be drawn like so. 

activity l

We’ll now go to activity M. This activity is preceded by activity I. Similarly, we can connect an arc from node 8 to 9 for activity N. 

activity m

Now, the network is complete! 

Now, to find the critical path. For this, we’ll need to find two values, Earliest Start Time (Es) and Latest Completion Time (Lc).

The process of determining the Es for all events is called a forward pass. 

The process of determining the Lc for all events is called a backward pass.

Let’s get into the forward pass. For this, first, we’ll need to create boxes at all nodes. These are then divided into two. The lower half of the box represents the earliest start time of the node, while the upper half represents the latest completion time. 

Your network diagram should look something like this. 


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For this, we’ll be using the formula, Esj = max (Esi + Dij)

Which when simplified, the earliest start time for the second node (head node), is the maximum of the combination of the earliest start time of the tail node and the duration between the two nodes. 

So, for node 1, the earliest start time is always zero. 

For node 2,
it would be, Es2 = 0 (earliest start time for node 1) + 3 (duration between 1 and 2) = 3


For node 3, 

it would be, Es3 = 0(Es1) + 4(D1 to 3) = 4


For node 4, we can see that two arcs connect to it. This means that we’ll need to choose among the largest of the two options available to us. 

Es4 = 0(Es0) + 6 = 6 or

Es4 = 4(Es3) + 3 = 7

We’ll choose 7 since it’s larger.


Similarly, we have three options to choose from when it comes to node 6. Since three arcs connect to it. 

Es6 = 3(Es2) + 1(D2-3) = 4

Es6 = 4(Es3) + 4(D3-6) = 8

Es6 = 7(Es4) + 5(D4-6) = 12

Hence we’ll select the last option since it’s the largest among the three. 


Now, for node 5. Since it’s directly connected to node 2, we can directly apply the formula. 

Es5 = 3(Es2) + 9(D2-5) = 12


Let’s take node 8. 

Es8 = 12(Es5) + 3(D5-8) = 15 or

Es8 = 12 (Es6) + 6(D6-8) = 18 

We’ll choose Es8 as 18 since it’s the larger of the two. 


Now for node 7. We can directly apply the formula to these nodes.

Es7 = 7(Es4) + 4(D4-7)  = 11


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Finally, we’ve got node 9.

It has 3 nodes connecting towards it. We’ll have to choose the maximum of the three. 

Es9 = 18(Es8) + 9(D8-9) = 27

Es9 = 12(Es6) + 3(D6-9) = 15

Es9 = 11(Es7) + 6(D7-9) = 17

We’ll choose the arc from node 8 since it’s got the highest value.  


And like that, the forward pass is complete. Now, for the second part of the critical path method.  Let’s take up the backward pass. For that’ we will be using the following formula. 

Lci = min(Lcj - Dij)

This, when put simply, means the latest completion time of the tail node is equal to the latest completion time of the head node minus the distance between the two. 

Let’s start from the final node, number 9. 

The Lc for this node will always be equal to its Es.
So, Lc9 = 27.


Next, let’s have a look at the latest completion time for the 8th node. Since it’s directly connected only to the 9th node, we can directly apply the formula mentioned earlier. 

Lc8 = 27(Lc9) - 9(D9-8) = 18


Now, let’s have a look at the latest completion time for node 7. Since there’s a direct connection between nodes 9 and 7. 

Lc7 = 27(Lc9) - 6(D9-7) = 21


Let’s move on to node 6. As we can see in the diagram, there are two points extending to nodes 8 and 9 from node 6. So we have two options to choose from. 

Lc6 = 18(Ls8) - 6(D6-8) = 12 or

Lc6 = 27(Ls9) - 3(D6-9) = 24 

We’ll choose the Lc of node 6 as 12.


We’ll now go to node 5. Since it’s directly connected to the 8th node, we can directly apply the equation.  

Lc5 = 18(Lc8) - 3(D5-8) = 15


Next up, let’s find the latest completion time for node 4. 

Since there are two connections extending from the node, to nodes 6 and 7 respectively, we’ll need to select the minimum between the two. 

Lc4 = 21(Lc7) - 4(D4-7) = 17

Lc4 = 12(Lc6) - 5(D4-6) = 7

We’ll choose 7 as the latest completion time for node 4. 


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Now for node 3. 

Since there are two nodes connecting from node 3 to nodes 4 and 6. So, we’ll need to choose between the 2. 

Lc3 = 12(Lc6) - 4(D3-6) = 8 or

Lc3 = 7(Lc4) - 3(D3-4)  = 4

We’ll choose 4 as the latest completion time for node 3. 


Let’s now go to node 2. Again, since there are two connections made from 2 to node 5 and 6, we’ll need to choose the minimum among the two. 

Lc2 = 15(Lc5) - 9(D2-5) = 6

Lc2 = 12(Lc6) - 1(D2-6) = 11

We’ll choose the latest completion time of 2, as 6.


And finally, we have node 1. 

Since there are connections to 2, 3, and 4 from 1, we’ll need to choose from the three.

Lc1 = 6(Lc2) - 3(D1-2) = 3

Lc1 = 4(Lc3) - 4(D1-3) = 0

Lc1 = 7(Lc4) - 6(D1-4) = 1

We’ll choose 0 as the latest completion time for the node.


And there we go! The backward pass is complete. 

Now, for the final step of the critical path method. To determine the critical path, there are three major criteria that need to be satisfied. 

Esi = Lci

Esj = Lcj

Esj - Esi = Lcj - Lci = Dij

From the diagram, we can see that nodes that satisfy the requirements are: 1, 3, 4, 6, 8, and 9. 

Hence the activities on the critical path are B - D - H - K - N.

final cpm

Hence the critical path is B + D + H + K + N = 4 + 3 + 5 + 6 + 9 = 27. 

And there we go! We’ve found the critical path! 

Pros and Cons of Ssing CPM

The pros and cons of the critical path method (CPM) are as follows:

Pros of Using CPM in Project Management

The pros of using CPM are as follows:

  • Effective Communication: All phases of a project's life span must be considered when creating critical path method schedules. The program's structure becomes more achievable and firm when the skills shared by various team members are integrated.
  • Easier to Prioritise Tasks: Project managers can more effectively prioritize tasks and estimate the float of each one by determining the critical path. Float indicates the amount of time a task may be put off before it affects when it will be completed. A lower float indicates a greater priority.
  • Accurate Scheduling: CPM is a popular and dependable methodology for enhancing the precision of project schedules. Several project managers utilize CPM with the Programme Evaluation and Review Technique (PERT), which supports teams in estimating overall project length. 
  • Better Visualisation: Gantt charts and CPM network diagrams, which show critical path timelines, can help project managers understand a project's timeline and progress more quickly. These visual tools allow them to understand a project's direction more intuitively than a less eye-catching alternative.

Cons of Using CPM in Project Management

Some of the cons of using the critical path method are as follows:

  • Multiple Complexities: Several moving elements and detailed computations are involved in the CPM. The software may automate the computations, but entering accurate data requires thorough research and leaves room for human error. 
  • Limited Applicability: Not every project type is suited to the critical path method. Projects requiring creativity, like product design or research work, that tend to come along in unforeseen forms fail to lend themselves well to CPM.
  • Less Understanding of Resources: The critical path method also lacks sufficient understanding of how resource limitations impact project schedules. The accessibility of equipment or labor resources is not considered in the network diagram or CPM schedule.

Step by Step Guide on How to Find the Critical Path With Examples

The time of essential and non-critical tasks can be used to identify the critical path. This is a list of the steps, along with examples.

  • List Activities

List all the venture exercises or errands essential to create the expectations utilising a work breakdown structure. The rest of the CPM is built on the list of activities provided in the work breakdown structure.

  • Identify Dependencies

Choose the occupations based on your work breakdown structure that is interconnected. This can identify any task that can be finished alongside other chores.

These task dependencies are based on the example mentioned above:

  • Task A is necessary for Task B.
  • Task B is necessary for Task C.
  • C and D can be carried out concurrently.
  • Task D is necessary for Task E.
  • Task F depends on Tasks C, D, and E.

An activity sequence, which will be utilised to identify the critical path, is a set of dependent tasks.

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  • Create a Network Diagram

The network diagram, a flowchart that depicts the order of tasks, must then be created from the work breakdown structure. Each task should be represented by a box, with task relationships shown by arrows.

Until the overall project timetable is determined, you will add other time-bound components to the network diagram.

  • Estimate Task Duration

You must first estimate each activity's length before determining the critical path, which is the longest series of critical tasks.

Try these to get a sense of the time:

  • Using knowledge and experience to make educated assumptions
  • Estimating using information from past projects
  • Estimating using established industry practices

Try the forward pass and backward pass technique instead:

  • Forward pass: This method uses a previously stated start date to determine early start (ES) and early end (EF) dates. ES is the direct ancestor with the highest EF value; EF is calculated as ES plus duration. The calculation begins at ES of the first action with 0 and moves forward through the schedule. Establishing ES and EF dates enables early resource allocation for the project.
  • A backward pass determines the dates for late starts (LS) and late finishes (LF). LF is the lowest LS value among immediate successors, and LS is LF - duration. The calculation begins with the final action on the timetable and works its way backward.

The scheduling flexibility of each activity can then be determined using the early and late start and end dates.

  • Calculate the Critical Path

Although the critical path can be determined manually, adopting a critical path algorithm can save time.

Below are the steps:

Step 1: Next to each action, note the start and end times.

The initial activity lasts for the allotted period and starts at 0.

The start time of the next activity is determined by the finish time of the previous one, and the end time is calculated by multiplying the start time by the duration.

Do this for each activity.

Step 2: To discover how long the entire sequence lasted, look at the last activity in the sequence's end time.

Step 3: The critical path is the series of operations that takes the longest time.

You can construct the entire project schedule around the critical path once it has been identified.

  • Calculate the Float

It illustrates how much extra time could be added to the task without impacting other activities or the project's deadline for completion.

The project's degree of flexibility can be determined by identifying the float. Use the resource known as "float" to cover project risks or unforeseen problems.

The dates of critical tasks are fixed since they have zero floats. Positive float tasks go on the non-critical route, where their delay won't affect the project's completion. Non-critical jobs might be skipped if you need more time or resources.

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Dealing with Contingencies and Constraints

Two ways to deal with contingencies and constraints in CPM are as follows:

Fast Tracking

Fast-tracking is the method of carrying out several tasks on the critical path while simultaneously minimizing the project's duration. Fast-tracking is feasible for tasks that lack "difficult" attachments or don't start completely dependent on previous tasks. Fast-tracking necessitates more resources. 


Crashing is a process of allocating additional resources to your project to complete it in a faster and more efficient way. Crash durations are effective in projects that would benefit from additional resources and can use some resources from tasks with higher floats. 

Critical Path Method Software

Programs or software specifically designed for project management that lets you create critical path schematics for a given project are called critical path software or CPM software. These tools make your daily activities easier by helping you analyze, schedule, and manage project tasks, reliance, and resources.

Here are some of the critical path method software: 

  • Office Timeline
  • Smartsheet
  • Zoho Projects 
  • LiquidPlanner
  • ProjectManager
  • Wrike
  • nTask
  • LucidChart

Features of Critical Path Software

The general features of critical path software are as follows:

  • Complete process visibility using Gantt charts and Kanban boards
  • Set a task, an overview of the task, assignees, and to-do lists
  • Interact on discussions or challenges to projects
  • Make dependencies between tasks
  • Set both the actual and projected dates
  • Control spending and produce a financial summary
  • Identify challenges and risks, eventually delegate them
  • Integrations by third parties
  • Track your tasks

Key Critical Path Terms for the PMP Exam

Some of the critical path terms which can be important for the PMP exam, which includes the question of what CPM is, are as follows: 

  1. Critical Path Method: It is a sequential managing projects approach for process development that distinguishes between essential and minor duties, thereby avoiding delays and workflow constraints.
  2. Critical Path DRAG: An essential action's total time adds to the project's overall duration. Alternatively, cutting the length of one essential activity to a minimum would shorten the time needed to complete the project.
  3. Criticality Index: It is employed in risk analysis, displaying how often a specific activity has been on the critical path throughout the study. High Criticality Index activities are more inclined to be placed on the critical path, which increases the likelihood that they will delay the project.
  4. Total Float: The amount of time that can be added to an activity's early start date yet to prevent the project as a whole from being pushed back.
  5. Free Float: The duration of a task can be postponed without pushing back the early start time of a succeeding task.
  6. Forward Pass: The strategy for figuring out the critical path method's early start or finish times for tasks.
  7. Backward Pass: The strategy to determine when an activity in the critical path method will have a late start or finish.
  8. Network Diagram: A diagram that shows the connections between project activities. It is typically created from left to right to symbolize the project's sequence.
  9. Network Analysis: Deconstructing a complex project into its various components (tasks, timelines, etc.) and then graphing those parts to show how they relate.

Total Float vs Free Float

Total float: This is the amount of time an activity can be postponed from the early start date before the project's completion date or a scheduling restriction is violated. Total float is equal to LS-ES or LF-EF.

Free float: The amount of time a task can be postponed without influencing the one after it. Only when two or more activities share a common successor can there be free float. This is the point where activity converges on a network diagram. ES (next task) - EF = free float (current task)

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How to Use the Critical Path Method

CPM gives you an insight into the status of your project and enables you to keep track of activities and their turnaround times. These are some additional uses for CPM.

Compress Schedules

There are situations when project deadlines may be advanced, but this could be better. In those circumstances, you can use either fast tracking or crashing as a schedule compression strategy.

Fast-tracking: Analyse the critical path to identify tasks that can be completed concurrently. The entire length will be shortened by using parallel processes.

Increasing resources is a step in the process of "crashing" operations. Be sure the additional resources will still fit inside the project's scope before acquiring them, and inform the stakeholders of any modifications.

Resolve Resource Shortages

Remember that the availability of resources is not taken into consideration by CPM. Therefore, you can employ resource-leveling tactics to resolve a resource deficit, such as an overbooked team member or a lack of equipment.

To ensure that a project can be finished with the currently available resources, these strategies work to alleviate resource over-allocation problems.

You should modify the critical route or use this strategy for activities that have floated since resource-leveling works by changing the start and end dates of the project.

Compile Data for Future Use

Since you're working with informed estimations for activity durations, the schedule generated by CPM is liable to alter. Therefore, as the project progresses, you can contrast the original critical path with the current one.

Future studies can use this information to predict work durations more precisely.

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Critical Path Method vs PERT

PERT estimates the time needed to perform tasks, but CPM is utilised when the activity durations have already been assessed. This is the fundamental distinction between PERT and CPM.

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Critical Path Method vs Gantt Chart

Horizontal bar charts, called Gantt charts, lay out project activities that may be monitored within a predetermined timeframe. The dependencies between tasks are displayed using both CPM and Gantt charts.

Here are some distinctions between the two tools:


  • Project duration is calculated, and critical and non-critical pathways are visualised.
  • Shown as a network diagram with connected boxes.
  • Does not indicate the resources needed
  • Plots activity without a time frame on a network diagram

Gantt Diagram

  • Visualises the development of project activity
  • Presented as a horizontal bar graph.
  • Demonstrates the resources needed for each action
  • Creates a timetable of activities

Gantt charts and CPM can be used in conjunction to monitor critical pathways over time and keep your project on schedule.

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What’s Next?

Now that you know the critical path method, you can go into some of the more complex concepts of project management. For that, we recommend signing up for the PMP® Certification Training, which prepares you for your PMP certification exam. When you use effective tools like Microsoft Excel templates, you can raise your career to a whole new level.

If you have any questions for us, please leave them in the comments section, and our team of experts will be happy to answer them for you at the earliest!


1. What is the critical path method example?

Any project that requires a flow of certain steps to finish can use the critical path method, such as building a house; each task would need some time and resources to complete and step into the next activity. 

2. What is the difference between CPM and PERT?

The differences between CPM and PERT are as follows:

  • PERT is a probability model, whereas CPM is a deterministic model.
  • PERT is used to manage uncertain project tasks, and CPM is used to manage certain project tasks.
  • PERT is a non-repetitive job, whereas CPM is a repetitive job.

3. Where is PERT used?

PERT calculates a realistic amount of time any project will take to complete. 

4. Why is critical path important?

It is crucial because it determines all the activities required to finish the project. It also indicates the tasks that are needed on time and can be delayed.

5. What is slack or float?

It is the amount of time for which any task can be delayed that would not lead to any delay to other activities or the projected completion time of the project.


About the Author

Rahul ArunRahul Arun

Rahul is a Senior Research Analyst at Simplilearn. Blockchain, Cloud Computing, and Machine Learning are some of his favorite topics of discussion. Rahul can be found listening to music, doodling, and gaming.

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