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Critical Path calculations are used to determine the critical path within a project.

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Quick reference

Critical Path Calculations

Critical Path calculations are the method used to determine the critical path within a project.

When to use

Normally, the critical path will be calculated by project management software once the project network diagram and task duration estimates have been entered into the software.  However, you cannot use software when taking the PMP® exam; so you must be able to calculate critical path manually.  I believe the method shown below is the easiest manual technique.

Instructions

  1. Create a project network diagram with all tasks. I create a box as shown above for each task in the network and draw arrows between boxes to show the relationships.                                                                           
  2.  Estimate task Duration for all tasks and put the duration in the center portion of the box.  I strongly recommend that you use consistent units.  If you are given a problem with different units, convert them to the same units before trying to calculate the critical path.
  3. Starting with the first task in the network, set the Early Start (ES) equal to zero.
  4. Add the Duration to ES to calculate Early Finish (EF) for the first task in the network.
  5. The value of EF for the first task is the value of ES for the next task in the network, just follow the relationship arrow(s).
  6. Continue to the end of the project adding a task duration to each task’s ES to determine that task’s EF.  Then follow the arrow to the next task.  If a task has multiple input arrows, use the highest value of EF from predecessor tasks to set the ES.  You have now completed the “forward pass.”  The critical path may be obvious to you at this time, but you need to do the next steps to determine the task total float.  Many questions relating to critical path will ask how much float is available for various tasks in the network.  So you need to continue on to do the “backward pass” and float calculations which are outlined in steps 7-11. 
  7. For the final task or milestone in the network, set the value for Latest Finish (LF) equal to the value of EF for that task.
  8. Subtract the Duration from LF to calculate the Latest Start (LS) for that last task or milestone.
  9. The value of LS for the last task is the value of LF for the next to last task, follow the network diagram arrow backwards.
  10. Continue subtracting the task duration from the LF for a task to determine the LS for that task until you have reached the beginning of the project.   This is referred to as the “backwards pass.”  If there are multiple arrows flowing back into a task, use the lowest value of LS from successor task to set the LF for that task.  The final value for LS that you calculate (which would be for the first task in the project) should equal zero.  If not you have made a mistake.
  11. Subtract the EF from LF for each task to determine the Task Total Float.
  12. Tasks with zero Float are on the critical path.

 

An example is shown below.  The examples used in the PMP® exam will likely be more complex than this.  Therefore, be sure to do the exercise so that you have practiced quickly calculating critical path and float.

PMP is a registered mark of the Project Management Institute, Inc.

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  • 00:05 Hi, I'm Ray Sheen.
  • 00:06 You can expect to need to calculate critical path on the PMP exam.
  • 00:10 Either to determine the critical path in a question, or
  • 00:13 to determine the amount of float associated with activities.
  • 00:16 In this lesson,
  • 00:17 we'll focus on the calculations and we'll talk more about float in another lesson.
  • 00:21 On the PMP exam, you'll not be able to use any software to help you
  • 00:26 calculate the critical path, so you must be able to do it manually.
  • 00:31 This technique is a relatively quick and simple technique for manual calculations.
  • 00:35 Start by creating a network diagram of the project and create one of these boxes for
  • 00:40 each item in the network.
  • 00:42 The top line of the box is the task or activity name.
  • 00:45 The center of the box is the duration of that task or activity.
  • 00:48 Something to watch for, be certain to use consistent units.
  • 00:52 Put everything in days, week, months, fortnight.
  • 00:56 Now, we will calculate the total schedule duration for the project.
  • 01:00 The top small box on the left side of the task box is for the Early Start, or ES.
  • 01:06 Set this box on the first task in the network to zero.
  • 01:10 This is the start of project time.
  • 01:13 The top small box on the right side of the task box is Early Finish, or EF.
  • 01:19 This value is set by adding the Duration to the Early Start.
  • 01:24 The Early Finish value is then used as the Early Start value for
  • 01:28 the next task in a network.
  • 01:30 This is because the next task can start as soon as the previous task is done.
  • 01:35 Continue this process all the way through the network diagram.
  • 01:39 If there are multiple predecessor tasks, the Early Start for
  • 01:43 the task is the largest value of Early Finish for the predecessor tasks.
  • 01:48 This means all of those predecessor tasks must be done before the task can start.
  • 01:53 So you must wait until the last one finishes.
  • 01:56 Once you have finished, you have completed the forward pass through the network.
  • 02:00 You may be able to recognize the critical path at this time, but
  • 02:04 we must do the backwards pass to be able to calculate the float.
  • 02:08 Let's look at that now.
  • 02:09 The lower small box on the right side of the task box is for latest finish.
  • 02:14 For the final task in the network diagram,
  • 02:17 set the latest finish to the value of early finish for that task.
  • 02:22 Since critical path is calculating the shortest path through the project, we have
  • 02:26 to look at the last step as being both the shortest and longest path in the process.
  • 02:32 Now for that task, subtract the duration value from the latest finish
  • 02:36 to determine the latest start for that task.
  • 02:40 The value for latest start for the last task is then used as the value for
  • 02:43 latest finished for the next to last task.
  • 02:47 Follow the network diagram arrows backwards through your project network.
  • 02:52 Continue working your way backwards through the network taking the latest
  • 02:56 start from one task and using it as the latest finish for the predecessor task.
  • 03:01 If a task has multiple successor tasks,
  • 03:03 it will have multiple arrows coming back into it.
  • 03:07 In that case, use the smallest value of latest start on the successor tasks for
  • 03:12 the latest finish on the predecessor task.
  • 03:15 Just to be clear, when there are multiple arrows on the forward pass,
  • 03:19 you use the largest value.
  • 03:21 When there are multiple arrows on the backwards pass, use the smallest value.
  • 03:26 Finally, subtract the early finish from latest finish to determine the task total
  • 03:30 float, and place that in the bottom box.
  • 03:33 Every task that has a 0 value for task total float is a critical path task,
  • 03:38 there will be at least one path that runs all the way from start to finish through
  • 03:42 the project.
  • 03:43 Let's do an example.
  • 03:45 This is a simple network and I've already put the task names and
  • 03:48 the duration in days in the appropriate boxes.
  • 03:52 The networks you'll see in the PMP exam will likely be
  • 03:54 a little more complicated than this.
  • 03:56 I will set the early start for Task A to 0.
  • 04:00 Now I do the forward pass of adding the duration early start to get a value for
  • 04:05 early finish.
  • 04:06 As we go across the top of the network, you see that in Task A,
  • 04:09 we start with 0, add 3 to get 3 for our early finish.
  • 04:13 The 3 goes to Task B as the early start and
  • 04:16 2 days are added to get an early finish for Task B of 5 days.
  • 04:20 The 5 goes to Task D, add 4 days to get 9.
  • 04:24 The 9 goes to Task F, add 3 days to get 12.
  • 04:27 The 12 goes to Task G, add 4 to get 16.
  • 04:31 But before we can do Task H, we need to do the lower path,
  • 04:36 since Task H has two arrows coming into it.
  • 04:39 So let's look at the lower path.
  • 04:41 The 3 from Task A goes to Task C, add 5 to get 8.
  • 04:45 The 8 goes to Task E, add 8 to get 16.
  • 04:48 The 16 goes to Task I, add 2 to get 18.
  • 04:53 Now for Task H.
  • 04:55 The early finish from Task F is 12 and the early finish from Task E is 16.
  • 04:59 We take the larger of those values, which is 16, for the early start for Task H.
  • 05:05 We add 6 to get 22.
  • 05:07 And for Task I, we have a 16 from Task G, a 22 from Task H, and an 18 from Task I.
  • 05:14 We take the 22, which is the largest value for the early start, and add 4 to get 26.
  • 05:19 The soonest this project can complete is 26 days from when it starts.
  • 05:25 Okay, that was the forward pass, now for the backward pass.
  • 05:29 For Task J,
  • 05:30 we set the latest finish value equal to the early finish value of 26 days.
  • 05:36 Subtract 4 from 26 to get a latest start of 22.
  • 05:40 This late start value is the late finish value for tasks G, H and I.
  • 05:46 Task G, 22 minus 4 is 18.
  • 05:49 Task H, 22 minus 6 is 16.
  • 05:52 Task I, 22 minus 2 is 20.
  • 05:55 Now, to continue backwards, we need to take the smaller of the late start values.
  • 06:01 For Task F, we have an 18 from G and a 16 from H, so we use the 16.
  • 06:07 We subtract three to get 13.
  • 06:08 For Task E, we have 16 from H and 20 from Task I, so we use the 16.
  • 06:14 We subtract 8 to get 8.
  • 06:18 Continuing on the top row, we take the 13 from Task F and
  • 06:21 use that on Task D, subtract 4 and we get 9.
  • 06:25 The 9 goes to Task B, 9 minus 2 is 7.
  • 06:29 On the bottom row, Task E send an 8 to task C, 8 minus 5 is 3.
  • 06:34 Now for Task A, there's a 7 at Task B and a 3 at Task C.
  • 06:39 The smaller of the two values is the 3, 3 minus 3 equals 0.
  • 06:44 And we find that we get back to 0 for the latest start of the first task.
  • 06:50 You should get back to 0.
  • 06:52 If you did not, you did your math wrong.
  • 06:54 The final calculation is to subtract the early finish from the latest finish for
  • 06:58 each task.
  • 07:00 By the way, if you ever have a negative value for
  • 07:02 that float, you did your math wrong.
  • 07:05 As we can see, we have a path with zero float.
  • 07:08 That, is the critical path.
  • 07:11 The forward pass and
  • 07:12 backwards pass, are the keys to determining your critical path and float.
  • 07:17 Now most of the time, you'll be using software to do this, but
  • 07:20 on the PMP exam, you have the privilege of doing it manually.

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