# How to calculate Float, Free Float, Total Float Using ES, EF, LS and LF

Float tells you about the flexibility you have as a project manager to deal with delays in activities that are not on the critical path without delaying the whole project.

In other words float tells the project manager how much extra time you have on activities which are not on critical path.

In this blog post, we will look at how to calculate float, total float, free float, early start, late start, early finish and late finish.

In order to understand this blog post, you need to be aware of the following concepts.

1. What type of dependencies exist the project management?
2. What is project schedule network diagram and how to create it?
3. What is critical path method (CPM)?
4. How to use critical path method (CPM) to find out the critical path in the project?
5. How to calculate float in project management using the simple method? Though in this chapter we will learn on how to calculate float using forward pass and backward pass.

In case if you are not aware of these concepts, please go through these concepts before reading this blog post. ## Float, Total Float, Free Float, Early Start, Late Start, Early Finish & Late Finish

In your project compared to critical path, other paths or very shorter. In that case the project manager has lot of flexibility to play with the activities which are not on the critical path.

Meaning that, if the float is high, then this will give the project manager room to play and use more resources towards the critical path activities.

Calculating Early start, late start, early finish and late finish helps the project manager to know, how early or late the activity can be started or finished.

Also in this blog post we will look at few important concepts such as how to calculate total float and free float.

So what are we waiting for?

Let us jump into the topic right away.

## Example of Network Diagram

For the purpose of this blog post we will take the below example of project schedule network diagram to find out float, total float, free float using the early start, early finish, late start and late finish. In order to find out the early start, early finish, late start and late finish, we will use the following activity node description. For the purpose of this example let us assume that activity duration is mentioned in number of days. So with this notations, initially with all the placeholders, the network diagram looks as follows. ## Steps To Calculate Float, Total Float And Free Float

Here are the steps we use to find the float, total float and free float using the early start, early finish, late start and late finish values.

1. Figuring out the critical path in the project
2. Finding out Early Start and Early Finish Using Forward Pass
3. Finding out Late Start and Late Finish Using Backward Pass
4. Calculating Total Float or Float
5. Calculating Free Float

## Figuring out the critical path in the project

For that, first we list down the paths available in the project.

Path 1 : START=> A => B => C => D => Finish

Path 2 : START=> E => F => D => Finish

Calculate length of each of the paths.

Path1 total duration = 5+6+2+8 =21

Path2 total duration = 2+3+8 =13

So as we learned critical path is the longest path in the project, path1 is the critical path.

## Finding out Early Start and Early Finish Using Forward Pass

We will use a technique called forward pass to find out early start and early finish. Forward pass simply means traversing through each activity node from left to right to find out early start and early finish.

Let us take path 1 first as this is the critical (longest) path in the project.

### Activity A

In path1, the first activity node after the start activity node is activity A. The early start of activity A is always “1” as this is start activity node. This indicates that the first activity starts on day 1.

Early finish of the activity node is how early the activity can be finished considering the early start and duration. So early finish is calculated as follows.

EF = ES + Duration -1

So for Activity A, EF = 1+5-1 =5

Sounds good. Let us now do the same for all the activities in path 1.

### Activity B

ES of activity B is calculated by adding 1 to the early finish of the predecessor activity.  So in this case for activity B, ES = 5+1 = 6 and EF = 6+6-1 = 12

### Activity C

ES of activity C is calculated by adding 1 to the early finish of the predecessor activity. So in this case for activity C, ES = 11+1 = 12 and EF = 12+2-1 = 13

### Activity D

Now the tricky part comes. For activity D, there are two predecessors. There are C and F. So to calculate early start of D, you need first calculate the early finish of both C and F and then take the latest (maximum) early finish among both C and F.

So the ES of D = Maximum of EF of activities C and F +1.

So for this we need to calculate ES and EF of activities in path2. (so holding on the activity D for the time being and going to path2 activities)

### Activity E

ES of activity E is 1 as is the first activity in this path after the start. And early finish (EF) of activity E =1+2-1 =2

### Activity F

ES of activity F is calculated by adding 1 to the early finish of the predecessor activity. So in this case for activity F, ES = 2+1 = 3 and EF = 3+3-1 = 5

Since we calculated both the predecessor of activity D, now go back to activity D again to complete the early start and early finish of activity D.

### Resuming Activity D

Early start of activity D is latest (maximum) of EF of both C and F +1.

Since 13 (EF of activity C) is greater than 5(EF of activity F), so we take EF of activity C +1 as the early start (ES) of activity D.

So ES of activity D = 13+1 =14 and EF=14+8-1=21

So after the forward pass, the network diagram looks as follows: Since we have finished the calculations of early start and early finish across all the paths in the project, now it is time to go for find out late start and late finish by using backward pass.

## Finding out Late Start and Late Finish Using Backward Pass

In the backward pass, you will start with the end activity node and traverse through backward till the start activity node in each path to find the late start and late finish for each of the activities in all the paths of the project.

### Activity D

So let us start at the end activity of path1, which is activity D. And calculate the late start and late finish of activity D.

LF of activity D is the same as the EF of activity D as this is the last activity in the project. So LF of activity D = 21.

LS of activity D = Late finish of activity D – duration +1

LS of activity D = 21 – 8 +1 = 14

### Activity C

For activity C, LF = LS of successor activity -1 = 14-1 = 13.

And LS of activity C = Late finish of activity C – duration +1 = 13-2+1=12

### Activity B

For activity B, LF = LS of successor activity -1 = 12-1 = 11.

And LS of activity B = Late finish of activity B – duration +1 = 11-6+1=6

### Activity A

For activity A, LF = LS of successor activity -1 = 6-1 = 5.

And LS of activity A = Late finish of activity A – duration +1 = 5-5+1=1

### Activity F

For activity F, LF = LS of successor activity -1 = LS of D -1= 14-1 = 13.

And LS of activity F = Late finish of activity F – duration +1 = 13-3+1=11

### Activity E

For activity E, LF = LS of successor activity -1 = 11-1 = 10.

And LS of activity E = Late finish of activity E – duration +1 = 10-2+1=9

So after completing the forward pass and backward pass, the completed network diagram looks as follows. ## Calculating Total Float or Float

We already learned in the previous blog post on how to calculate float in a simple way. Now we will see how to calculate float using the early start, late start, early finish and late finish value, we just calculated.

Also we have learned that SLACK is a word used as an alternative to FLOAT.

TOTAL FLOAT is also another word used to represent the float.

As per the PMBOK Guide, the total float is “the amount of time that the activity can be delayed without delaying the whole project”.

Total Float of an activity =  Late Start of an activity – Early Start of an activity

or

Total Float of an activity =  Late Finish of an activity – Early Finish of an activity

In this case total float of activity E and F are 8.

Also we have learned that the total float of the activities on the critical path is always equals to ZERO, by definition.

That is why if you see the above completed network diagram, in the critical path the late finish and early finish are referring to the same number. In the same way late start and early start are referring to the same number.

## Calculating Free Float

Free float is different from total float.

As per PMBOK guide, free float is defined as “the amount of time that a schedule activity can be delayed without delaying the early start date of any successor or violating a schedule constraint”.

So free float not just considers that the project is on time, but also considers the successor activity is on time.

So in this case,

Free Float  =  ES of the successor activity  – EF of the current activity

Free Float of activity E = 3 – 2 =1

Free float of activity F = 14-5 = 9

With these number what can we understand about free float?

As free float of activity E is 1, indicating that the activity E can slip maximum by 1 day without impacting the timelines of it successor activity F.

In the same way, free float of activity F is 9, indicating that the activity F has luxury or flexibility of slipping 9 days, without impacting the timelines of its successor activity D. In the above mentioned completed network diagram, you can observe that activity F any way have to wait, until activity C also finishes for activity D to start.

## Conclusion

This is really a long post, to cover various calculation such as float, total float, free float, early start, early finish, late start and late finish using the forward and backward pass.

In the PMP exam, you may get some questions asking to find any of the above calculations.

Although these may seem a bit ambiguous, if you understand the concepts well, it is very easy to solve the questions on the PMP exam.

Let me know, if you have any queries or feedback on this blog post.

3 Responses to “How to calculate Float, Free Float, Total Float Using ES, EF, LS and LF”
1. Jia.Z September 19, 2018
• Ravi September 20, 2018
2. Michael December 23, 2018