---
title: "Total float and independent float"
subject: "Project Engineering"
chapter: 3
key: "semester_7/project_engineering:total-float-independent-float"
source: https://www.bctengineer.com/q/semester_7/project_engineering/total-float-independent-float
site: BCT Engineering
---

# Total float and independent float

Project Engineering · Chapter 3: Project Planning and Scheduling

- Asked in: 2074 Chaitra, 4 marks
- Video: [Total Float, Free Float and Independent Float explained with examples](https://www.youtube.com/watch?v=bChK4u34RD8) — PMC Lounge
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/project_engineering/total-float-independent-float
- Whole chapter: https://www.bctengineer.com/md/semester_7/project_engineering/chapter-3

## Question

Explain total float and independent float.

## Short answer

Total float is the maximum delay allowed without delaying project completion (LST–EST). Independent float is the delay possible when all predecessors finish as late as possible and successors start as early as possible, calculated as max(0, min(EST of successors) – max(LFT of predecessors) – D). For activity D with duration 2, TF = 3 days and IndF = 3 days.

## Answer

#### Total float

**Total float (TF)** is the maximum time by which an activity can be delayed without delaying the completion of the project. It is shared with the other activities on the same path.

$$
TF = LST - EST = LFT - EFT
$$

#### Independent float

**Independent float (IndF)** is the time available for an activity when its predecessors finish at their latest time and its successors start at their earliest time. Using it affects no other activity, so it is the safest float.

$$
IndF = \max\left(0,\ \min(EST_{succ}) - \max(LFT_{pred}) - D\right)
$$

#### Example

Example network (days): A = 4 and B = 3 are start activities; C = 5 and D = 2 follow A; E = 3 follows C and D; F = 4 follows B. Project duration = 12 days.

| Activity | D | EST | EFT | LST | LFT | TF | FF | Int.F | Ind.F |
|---|---|---|---|---|---|---|---|---|---|
| A | 4 | 0 | 4 | 0 | 4 | 0 | 0 | 0 | 0 |
| B | 3 | 0 | 3 | 5 | 8 | 5 | 0 | 5 | 0 |
| C | 5 | 4 | 9 | 4 | 9 | 0 | 0 | 0 | 0 |
| D | 2 | 4 | 6 | 7 | 9 | 3 | 3 | 0 | 3 |
| E | 3 | 9 | 12 | 9 | 12 | 0 | 0 | 0 | 0 |
| F | 4 | 3 | 7 | 8 | 12 | 5 | 5 | 0 | 0 |

Activity D: $TF = 9 - 6 = 3$ days. Its predecessor A is critical (LFT = 4) and its successor E starts at 9, so $IndF = 9 - 4 - 2 = 3$ days: D can move 3 days without affecting any other activity.
Activity B: $TF = 8 - 3 = 5$ days but $IndF = 3 - 0 - 3 = 0$, since F starts as soon as B finishes; the float is shared with F.

| | Total float | Independent float |
|---|---|---|
| Effect | May reduce float of other activities | Does not affect any other activity |
| Value | Larger or equal | Smaller or equal (never more than TF) |
| Basis | LFT - EFT | Successor EST - predecessor LFT - D |

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How is total float defined?
   A. LST - EST or LFT - EFT, the delay allowed without delaying the project
   B. Successor EST - EFT
   C. Successor EST - predecessor LFT - D
   D. Duration of the critical path
   Answer: A. Total float is shared with other activities on the same path. (Key point: Total float)

2. Why is independent float the safest float?
   A. It is always larger than total float
   B. Using it affects no other activity
   C. It is shared with successors
   D. It applies only to critical activities
   Answer: B. It assumes predecessors finish at latest and successors start at earliest. (Key point: Independent float)

3. How do independent float and total float compare?
   A. Independent float is always larger
   B. They are always equal
   C. Independent float is never more than total float
   D. Independent float is negative
   Answer: C. IndF <= FF <= TF. (Key point: Relation)

4. In the example, why is IndF of B zero although TF is 5 days?
   A. B is a critical activity
   B. B has zero duration
   C. B has no predecessor
   D. F starts as soon as B finishes, so the float is shared with F
   Answer: D. IndF = 3 - 0 - 3 = 0. (Key point: Activity B)

## Related in Project Engineering

- [Dummy activity and float definitions](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Afloat-definitions-dummy) — Project Engineering, chapter 3
- [CPM network, 9 activities with successors](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acpm-network-nine-act-a76) — Project Engineering, chapter 3
- [CPM network, 10 activities with successors](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acpm-network-ten-act-a74) — Project Engineering, chapter 3
- [CPM network, 10 activities (A=4 to J=9)](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Acpm-network-ten-act-as70) — Project Engineering, chapter 3

## Related in other subjects

- [CPM schedule, critical path and float](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_engineering_and_management%3Acpm-network-critical-path-float) — Industrial Engineering and Management, chapter 3