Total Float
Total float is what we are aware of, and is commonly referred to as a float.Total float is the amount of time that an activity can be delayed without delaying the project completion date. On a critical path, the total float is zero.
Total float is often known as the slack.
You can calculate the total float by subtracting the Early Start date of an activity from its Late Start date (Late Start date – Early Start date), or Early Finish date from its Late Finish date (Late Finish date – Early Finish date).
Free Float
Now we come to free float. This is going to be a bit different, and might be new to you!Free float is the amount of time that an activity can be delayed without delaying the Early Start of its successor activity.
You can calculate the free float by subtracting the Early Finish date of the activity from the Early Start date of next activity (ES of next Activity – EF of current Activity).
Keep in mind that if an activity has only one successor activity, free float and total float will be the same.
However, if an activity has more than one successor activity, it may have a different free float.
A note on convention used in the example:
There is disagreement whether the first day of the project should be “1” or “0”.In fact, both conventions are correct, and you are free to choose what you like. I choose to start my project from day “1”.
The following are my reasons for doing so:
- This convention is followed the PMBOK Guide.
- It seems more logical to me to say, “Hey, today is my first day of the project!” instead of saying, “Hey, today is my zero day of the project.”
Since mathematically these two situations are different, the formula to be used to calculate the free float will also be slightly different. Don’t worry; the result is same in both cases.
If you choose to start your project from day 1
Free float of Activity X = Early Start of next Activity – Early Finish of Activity X – 1If you choose to start your project from day 0
Free float of Activity X = Early Start of next Activity – Early Finish of Activity XThe difference between these two formulas is very easy to remember. If you start from day “1,” you have to subtract “1” from the formula.
If you start from day “0”, there is no need to subtract “1.”
Now we will move on to the examples. I will start with a simple example, and then go on to a more complex situation.
While giving you these examples, I’m assuming that you’re aware of drawing a network diagram, identifying the critical, and calculating the Early Start, Early Finish, Late Start, and Late Finish dates of activities.
Don’t worry, if you’re having problems with these calculations, I have written a blog post on the critical path method explaining all these things. Please visit this blog post to understand these concepts better and then come back here again.
Visit: Critical Path Method
Okay, let’s get started.
Example: 1
In the above network diagram, we have two paths:
- The first path is A->B->D with 20 days duration, and
- The second path is A->C->D with 12 days duration.
Calculating the Total Float
As we can see, the given diagram has only two paths, path A->B->D and path A->C->D.The path A->B->D is a critical path; therefore it will not have a total float.
Since the path A->C->D is a non-critical path, it can have a total float.
You have two methods to calculate the total float. In the first method, you subtract the duration of the non-critical path from the critical path.
In the second method, you find the total float for any activity by subtracting the Early Start date from the Late Start date(LS – ES), or subtracting the Early Finish date from the Late Finish date (LF – EF) on any activity.
The first method of finding the Total Float
Total float = duration of the critical path – duration of the non-critical path= (duration of the path A->B->D) – (duration of the path A->C->D)
= 20 – 12
= 8
Hence, the total float is 8 days.
The second method of finding the Total Float
On the path A->C->D, Activity A and D lie on the critical path; therefore, they will not have a total float. Only Activity C can have a total float.As stated earlier, we can calculate the total float by using either finish dates or start dates. Here, I will show you both ways to find it.
First we will go with the Late Finish and Early Finish dates:
Total float for Activity C = (LF of Activity C– EF of Activity C)
= 15 – 7
= 8
Now, the second formula:
Total float for Activity C = (LS of Activity C – ES of Activity C)
= 14 – 6
= 8
So both durations are the same, which means both formulas will provide you with the same result.
Calculating the Free Float
From the figure, you can see that only Activity C can have a free float, because other activities are lying on the critical path.Let’s find it.
Free float of Activity C = ES of next Activity – EF of Activity C – 1
= 16 – 7 – 1
= 8
Hence, the free float for activity C is 8 days.
Now it is time to move on to a more complex example.
Example: 2
For the below given network diagram, identify which activities can have a free float and calculate the free and total float for those activities, considering duration in days.
We know that,
Free float = ES of next Activity – EF of current Activity – 1
In the above diagram, Activity D and G can have the free float because only these activities have more than one successor activities.
Now since these activities have two successors, which activity will you select to use in the formula?
You will select the activity with the larger Early Start date.
Free Float for Activity D
Activity D has two successors: Activity B and E. Activity B has a larger Early Start date than Activity E. Therefore, we will select the Early Start of Activity B.Free float for activity D = ES of Activity B – EF of Activity D – 1
= 11 – 5 – 1
= 5
Total Float for Activity D
We know that,Total float = Late Finish of Activity – Early Finish of Activity
Or
Total float = Late Start of Activity – Early Start of Activity
Since we can use any of the formulas to calculate total float for the Activity D, we can go with the first formula.
Total float for Activity D = Late Finish of Activity D – Early Finish of Activity D
= 10 – 5
= 5
Have you noticed that the total float and free float for Activity D is the same?
This is just a coincidence; they need not to be the same. They can be different.
Free Float for Activity G
Again, activity G has two successor activities: Activity E and H. Since the Early Start date of Activity E is greater than the Early Start date of Activity H, we will choose Activity E to determine the free float for Activity G.Hence,
Free float of activity G = Early Start of Activity E – Early Finish of Activity G – 1
= 6 – 3 – 1
= 2
Total Float for Activity G
Total float for Activity G = Late Finish of Activity G – Early Finish of Activity G= 18 – 3
= 15
You see here that the free float for Activity G is 2 days, and the total float is 15 days, both are different.
Please note: if in the exam you’re asked to calculate the float for any activity, you have to calculate the total float. Total float is commonly referred to as a float.
Total Float vs. Free Float in CPM
Total Float: The total amount of time that a schedule activity
may be delayed from its early start date without delaying the project
finish date, or violating a schedule constraint.
Free Float: The amount of time that a schedule activity can be delayed without delaying the early start date of any immediately following schedule activities.
Now we'll look at the example. Refer to the Network Diagram in the figure first. I'm assuming that you know how to work with a Network Diagram and how to calculate Early Start, Early Finish, Late Start and Late Finish for activities on a Network Diagram.
Problem: What is the Total Float and the Free Float for Activity F and J?
Solution: Formulas:
The calculations are really simple.
For Activity F:
For Activity J:
Note: Free float can only occur when two or more activities share a common successor, or in other words, when activities converge on a Network Diagram. In our example, only activities F and J can have Free Float.
Free Float: The amount of time that a schedule activity can be delayed without delaying the early start date of any immediately following schedule activities.
Now we'll look at the example. Refer to the Network Diagram in the figure first. I'm assuming that you know how to work with a Network Diagram and how to calculate Early Start, Early Finish, Late Start and Late Finish for activities on a Network Diagram.
Solution: Formulas:
Total Float = LF - EF (or LS - ES)
Free Float = ES of next activity - EF
The calculations are really simple.
For Activity F:
Total Float = LF of F – EF of F => 8 – 5 = 3
Free Float = ES of G – EF of F => 5 – 5 = 0
For Activity J:
Total Float = LF of J – EF of J => 8 – 3 = 5
Free Float = ES of G – EF of J => 5 – 3 = 2
Note: Free float can only occur when two or more activities share a common successor, or in other words, when activities converge on a Network Diagram. In our example, only activities F and J can have Free Float.
