As students, we have to deal with assignments, exams, presentations, projects and more to make it through the semester. And when it comes to tasks such as calculating the critical path, probabilities, elaborating a PERT chart, and crashing projects, we may not even have time to eat. But what if you had access to an application to help you solve these types of exercises? Then you would have more time to dedicate to you and your loved ones. In this article we will explain everything about our **critical path method calculator**, and **PERT CPM diagram online**.

## PERT CPM Diagram - Free Version

The above application is a simplified version of our critical path method online calculator; it shows you the final result of the critical path, as well as the total time of the project. It is limited to 10 activities and is very useful to check the results of the problems you have to solve.

## Advanced Functions of Critical Path Calculator and PERT Chart Online

Within PMCalculators, we believe that your time and your learning are two valuable resources for your professional and personal development; in that sense, we have been striving to provide premium tools to all students who have a membership with us. Being project management one of the most requested topics by students, we have developed several project calculators with advanced functions that will allow you to learn the following:

- Draw the activity diagram in project nodes, as well as calculate the critical path for up to 50 activities.
- Calculate the early start and early finish times, late start and late finish times, and slack using the CPM method (ES, EF, LS, LF and slack time calculator).
- Obtain the standard deviation, variance and estimated time of each activity with the PERT method.
- Calculate the probability of finishing over or under schedule on a given project.
- Evaluate the cost of crashing a project.
- Reduce the project duration to the maximum possible.

All these functionalities are contained in 4 online calculators:

- Critical Path Calculator – CPM Network Diagram Generator (see example).
- PERT Chart Calculator and Critical Path (see example).
- Project Completion Probability – PERT Analysis Calculator (view example).
- Project Crashing Calculator (see example).

You will be able to access these applications and more student resources by joining our membership.

## How to use the critical path method calculator and online PERT CPM diagram

Note: The graphs that are generated with our applications are of activity on node. At the moment we do not generate diagrams of activities on arrows:

To use our tool (pro version) we will follow the following steps:

- Choose the calculator to be used according to the type of exercise to be solved (PERT calculator, CPM calculator, probability PERT or crashing project).
- Enter the number of activities for the exercise (For a graphic display issue, we suggest that it enter a
**maximum of 50 activities**). - Record the data of the precedents of each activity and its duration.
- Click on solve. The page will validate if the data entered is correct. If there is an error, it will show a message at the bottom.
- If the data entered is valid, the problem results will be calculated and displayed:
- A table with the details of the relationships between each activity.
- The graph of the
**PERT CPM diagram**. Clicking on the nodes display the data for each activity. You can also move the nodes to place them in a more suitable position. - The red nodes represent the critical path. You can save the image to computer by right clicking on the graphic.
- It will generate a schedule with the problem data which you can download as an image.
- It will display the table with the data of early start (ES), early finish (EF), late start (LS), late finish (LF) and slack (float).
- If the project needs to be crashed, the cost table and its iterations will be displayed.
- The total results of the exercise were shown in a blue box.

We will see its use with an example:

### Example

A small project consisting of eight activities has the following characteristics:

Activity |
Preceding activity |
Most optimistic time (weeks) |
Most likely time (weeks) |
Most Pessimistic time (weeks) |

A | – | 2 | 4 | 12 |

B | – | 10 | 12 | 26 |

C | A | 8 | 9 | 10 |

D | A | 10 | 15 | 20 |

E | A | 7 | 7.5 | 11 |

F | B,C | 9 | 9 | 9 |

G | D | 3 | 3.5 | 7 |

H | E,F,G | 5 | 5 | 5 |

- Draw the PERT network for the project.
- Prepare the activity schedule for the project.
- Determine the critical path.

### Solution:

We chose the PERT calculator:

We enter the number of activities:

Later we record the problem data:

By clicking on solve we will obtain the detail of relationships between each activity:

This table serves as a guide to build our **PERT CPM diagram**. It added two dummy activities to show the start and end. The activities with **0 (zero) slack** are the ones that make up the **critical path**.

### PERT CPM diagram

Clicking on the node shows more details:

Likewise, a schedule of activities is generated with the problem data. It takes the current day as the start date when solving the problem.

The following table presents the results to determine the critical path:

**Early Start (ES):**It is equal to the Early Finish to the activity's precedent. If it has more than one precedent, the highest value is taken.**Early Finish (EF):**It is equal to the Early Start of the activity plus its duration (t). EF = ES + t.**Late Start (LS):**It is equal to the Late Finish minus its duration (t). LS = LF – t.**Late Finish (LF):**It is equal to the late start of the activity that follows. If it has more than one successor, the lowest value is taken.**Slack – Float (S):**It can be calculated in two ways. S = LS β ES = LF β EF. Activities with zero slack make up the critical path and are highlighted in green.

**Estimated Time:**T_{e}= (T_{o}+ 4ΓT_{m}+ T_{p}) Γ· 6**Standard Deviation:**Ο = (T_{p}– T_{o}) Γ· 6**Variance**= Ο^{2}**Project variance**= Ξ£Ο_{i}^{2}. i=Activities that belong to the critical path. In the case of several critical paths, the one with the greatest variance is chosen.

To understand the concepts applied in our critical path online tool, we recommend that you review the following articles:

## Final reflection

Having access to this application while you take your project courses will save you a lot of time in your homework, as well as help you learn these concepts better so you can ace your exams. Do not hesitate to contact us if you have any questions or doubts.