Total Float and Free Float

Why Total Float and Free Float Matter

Float is the single most important concept in Critical Path Method (CPM) scheduling, and it sits at the heart of the Time Management domain of the CMAA Certified Construction Manager (CCM) exam. Float tells a Construction Manager (CM) how much scheduling flexibility exists, which activities can slip without harming the project, and which activities must be protected at all costs. In practice, float drives resource leveling, crew sequencing, subcontractor coordination, delay analysis, time impact analyses (TIAs), and the resolution of time extension claims. Disputes over who owns float are among the most common schedule-related conflicts on construction projects, so a CM who cannot calculate and interpret float cannot credibly review a contractor's schedule, evaluate a delay claim, or advise an owner on recovery options.

On the CCM exam you can expect float to appear in several forms: direct definition questions, calculation questions based on a small network, interpretation questions (what does negative float mean?), and judgment questions about float ownership and the CM's responsibilities when float erodes. Mastering this topic is therefore both a scheduling skill and an exam-scoring opportunity.

What Float Is

Float (also called slack) is the amount of time an activity can be delayed before it causes a problem. The two forms you must know cold are:

Total Float (TF) is the amount of time an activity can be delayed from its early start without delaying the project completion date (or a contractually imposed milestone). Total Float is a property of a path, not just a single activity: activities on the same non-critical path share the same pool of Total Float. If one activity consumes it, the downstream activities on that path lose it.

Free Float (FF) is the amount of time an activity can be delayed from its early start without delaying the early start of any immediate successor activity. Free Float belongs to the activity alone; using it does not affect anyone downstream. Free Float is the more conservative, more 'private' measure of flexibility.

Related terms that appear on the exam:

Critical Path: the longest path through the network, which determines the earliest possible project completion. Activities on the critical path have the lowest Total Float in the network, typically zero. Any delay to a critical activity delays the project.

Near-Critical Path: a path with very little Total Float (often defined as a few days or less). Near-critical activities deserve close monitoring because a small slip converts them into critical activities.

Negative Float: occurs when an activity's late dates are earlier than its early dates, meaning the schedule cannot meet a required completion date or constraint. Negative float signals that the project is behind and that recovery or acceleration is needed.

Project Float (Terminal Float): the difference between the scheduled completion date produced by the CPM calculation and the contractually required completion date. For example, if the CPM finishes on day 180 and the contract requires completion by day 200, the project float is 20 days.

Interfering Float: the portion of Total Float that is not Free Float (TF minus FF). Using interfering float delays a successor's early start even though it does not delay the project.

Independent Float: the float available to an activity even if all predecessors finish as late as possible and all successors start as early as possible. This appears less often on the CCM exam but should be recognized.

How Float Works: The CPM Calculation

Float is derived from the four dates produced by CPM time analysis:

Early Start (ES): the earliest an activity can begin, given its predecessors.
Early Finish (EF): ES plus duration.
Late Finish (LF): the latest an activity can finish without delaying the project.
Late Start (LS): LF minus duration.

These dates come from two passes through the network:

Forward Pass (left to right): calculates ES and EF. An activity's ES equals the largest EF among its predecessors (for finish-to-start relationships with no lag). EF = ES + Duration.

Backward Pass (right to left): calculates LF and LS. An activity's LF equals the smallest LS among its successors. LS = LF minus Duration. The final activity's LF is set equal to its EF (or to the contractual completion date, if the question specifies one).

The Formulas

Total Float = LS minus ES (equivalently, TF = LF minus EF). Both versions give the same answer; use whichever dates you have.

Free Float = ES of the earliest successor minus EF of the activity (for finish-to-start logic with zero lag, using the zero-based or 'end of day' convention). If a lag exists, subtract the lag as well. If an activity has multiple successors, use the successor with the smallest ES.

Convention warning: Some texts and software use a calendar-day (one-based) convention in which an activity starting on day 1 with a 3-day duration finishes on day 3, and the successor starts on day 4. Under that convention, Free Float = ES(successor) minus EF minus 1. The Total Float formula (LS minus ES) is unaffected by the convention. Always read the question for its convention; CMAA exam questions generally make this clear or use the simpler zero-based approach.

Key rules you can rely on:
1. Free Float can never exceed Total Float (FF is less than or equal to TF).
2. Critical path activities normally have TF = 0 and FF = 0.
3. The last activity on a non-critical path (the one that merges back into the critical path) typically has Free Float equal to its Total Float.
4. Activities earlier on a non-critical chain often have Total Float but zero Free Float, because any slip pushes the next activity on the chain.
5. Total Float is shared along a path; Free Float is not.

Worked Example 1: Basic Network

Activities and durations: A (3 days), B (4 days), C (2 days), D (5 days). Logic: A precedes both B and C; B and C both precede D. All relationships are finish-to-start with zero lag. Zero-based convention.

Forward pass:
A: ES 0, EF 3
B: ES 3, EF 7
C: ES 3, EF 5
D: ES 7 (largest of B's EF 7 and C's EF 5), EF 12

Project duration = 12 days.

Backward pass:
D: LF 12, LS 7
B: LF 7 (D's LS), LS 3
C: LF 7 (D's LS), LS 5
A: LF 3 (smallest LS of B and C = 3), LS 0

Total Float (LS minus ES):
A: 0 minus 0 = 0
B: 3 minus 3 = 0
C: 5 minus 3 = 2
D: 7 minus 7 = 0

Critical path: A, B, D.

Free Float of C: ES of successor D (7) minus EF of C (5) = 2. Here C's Free Float equals its Total Float because C merges directly into the critical path.

Worked Example 2: When Total Float and Free Float Differ

Modify the network: A (3) precedes B (4) and C (2); C precedes E (1); B and E both precede D (5).

Forward pass:
A: ES 0, EF 3
B: ES 3, EF 7
C: ES 3, EF 5
E: ES 5, EF 6
D: ES 7 (larger of B's 7 and E's 6), EF 12

Backward pass:
D: LF 12, LS 7
B: LF 7, LS 3
E: LF 7, LS 6
C: LF 6 (E's LS), LS 4
A: LF 3, LS 0

Total Float: A = 0, B = 0, C = 1, E = 1, D = 0.

Free Float:
C: ES of E (5) minus EF of C (5) = 0
E: ES of D (7) minus EF of E (6) = 1

Interpretation: C has one day of Total Float but zero Free Float. If C slips one day, the project still finishes on day 12, but E is forced to start a day later and loses its float. The one day of float is shared by C and E; whoever uses it first takes it from the other. This is exactly the real-world dynamic that causes disputes between trades.

Float in Construction Management Practice

Float Ownership. Unless the contract says otherwise, the prevailing industry position is that float is a shared project resource available on a first-come, first-served basis to whichever party (owner or contractor) needs it first. Many owners insert clauses stating that float is not for the exclusive benefit of either party. Some contractors argue they own float because they created the schedule. The CM should know what the contract says and ensure the specifications address float ownership explicitly to reduce claims.

Time Extension Analysis. A delay generally warrants a time extension only if it affects the critical path, that is, only if it consumes all available Total Float and pushes the completion date. An owner-caused delay to an activity with ample Total Float typically does not entitle the contractor to additional time, although it may still have cost consequences if it disrupts planned resource use.

Schedule Monitoring. During schedule updates, the CM tracks float erosion. A trend of shrinking Total Float on multiple paths is an early warning of a late project even before any activity becomes critical. Negative float in an update means the contractor must submit a recovery schedule.

Resource Leveling. Schedulers deliberately shift non-critical activities within their float to smooth labor and equipment demand. Activities with Free Float are the safest to shift because moving them affects no one else.

Sequestered or Hidden Float. Contractors sometimes pad durations, add preferential logic, or impose constraints to hide float so that it is not available to the owner. A CM reviewing the baseline schedule should question excessive constraints, unusually long durations, and logic ties that are not technically required.

Exam Tips: Answering Questions on Total Float and Free Float

Tip 1: Memorize the definitions by their reference point. Total Float is measured against the project completion date. Free Float is measured against the early start of the next activity. If a question asks how long an activity can be delayed without delaying the project, it is asking for Total Float. If it asks how long it can be delayed without affecting any successor, it is asking for Free Float.

Tip 2: Always do the forward and backward passes in order. Do not try to eyeball float. Write ES and EF above each activity and LS and LF below. For merge points, remember: forward pass takes the largest predecessor EF; backward pass takes the smallest successor LS. Reversing these two rules is the most common calculation error.

Tip 3: Use TF = LS minus ES as your default. It works in every convention and is the easiest to verify. Check your answer with LF minus EF; the two must match.

Tip 4: For Free Float, look only at the immediate successor. Take the smallest ES among all direct successors and subtract the activity's EF (and any lag). Do not look further downstream; that is Total Float territory.

Tip 5: Apply the sanity checks. Free Float can never be larger than Total Float. Critical activities have zero float. If your answer for FF is greater than TF, you have made an arithmetic error. If the longest path does not show zero float, recheck the backward pass.

Tip 6: Watch the day-counting convention. If the question says an activity starts on day 1 and finishes on day 3 with a 3-day duration, it is using the calendar-day convention, and Free Float = ES(successor) minus EF minus 1. If activities are shown starting at time 0, use the straightforward subtraction. When in doubt, Total Float questions are safer because the formula is unaffected.

Tip 7: Understand shared float conceptually. Exam questions often describe a scenario rather than a network: for example, 'Activity X has 5 days of Total Float and 0 days of Free Float. What happens if X is delayed 3 days?' The correct response is that the project is not delayed but the successor's early start shifts 3 days and the remaining shared float on that path drops to 2 days.

Tip 8: Know what negative float means and what the CM should do. Negative float means the schedule cannot meet the required date. The correct CM action is to require a recovery schedule, evaluate acceleration or resequencing, and notify the owner; it is not to simply extend the completion date.

Tip 9: Float and time extensions. If a question describes an owner delay to an activity that has sufficient Total Float, the correct answer usually is that no time extension is due because the critical path was not affected. If the delay exceeds the available Total Float, the extension equals the amount by which the delay exceeds the float.

Tip 10: Float ownership questions. Unless the contract language in the question says otherwise, the expected answer is that float is a shared project resource available on a first-come, first-served basis, and that the contract should define float ownership to avoid disputes.

Tip 11: Read for distractors. Answer choices often include the project duration, a predecessor's float, or Free Float when Total Float was asked. Reread the question stem before selecting an answer to confirm which float and which activity are being requested.

Tip 12: Manage your time. Network calculation questions can be lengthy. Draw a quick box diagram, fill in the four dates methodically, and move on. If you are running short on time, remember that the critical path activities have zero float, which lets you eliminate wrong answers quickly.

Practice Questions

Question 1. Activity M has ES = 10, EF = 14, LS = 13, LF = 17. Its only successor, Activity N, has ES = 14. What are the Total Float and Free Float of M?
Answer: TF = LS minus ES = 13 minus 10 = 3 days. FF = ES(N) minus EF(M) = 14 minus 14 = 0 days. M can slip 3 days without delaying the project, but any slip delays N.

Question 2. An owner-caused delay holds Activity P for 6 days. Activity P had 4 days of Total Float before the delay. How much time extension, if any, is the contractor entitled to?
Answer: The delay consumed the 4 days of float and pushed the critical path by 2 days, so the contractor is entitled to a 2-day extension (subject to contract notice requirements and float ownership language).

Question 3. Which statement is correct? (a) Free Float is always greater than Total Float. (b) Total Float is shared among activities on the same path. (c) Critical activities have the largest float. (d) Free Float is measured against the project completion date.
Answer: (b). Total Float is shared along a path. Free Float is never greater than Total Float, critical activities have the least float, and Free Float is measured against the successor's early start.

Question 4. A schedule update shows minus 5 days of Total Float on the critical path. What does this indicate and what should the CM do?
Answer: The project is forecast to finish 5 days after the required completion date. The CM should require the contractor to submit a recovery plan showing how the 5 days will be regained through resequencing, added resources, or extended work hours, and should notify the owner of the forecast and its implications.

Summary

Total Float measures how long an activity can slip without delaying the project; Free Float measures how long it can slip without delaying its immediate successor. Both are derived from the forward and backward passes of CPM: TF = LS minus ES (or LF minus EF), and FF = ES of the earliest successor minus the activity's EF. Free Float never exceeds Total Float, critical activities have zero float, and Total Float is shared along a path while Free Float is not. For the CCM exam, work calculations methodically, apply the sanity checks, read for which float and which activity is being asked, and connect float to the practical CM issues of time extensions, float ownership, negative float recovery, and schedule monitoring. A candidate who can do all of this will handle every float question the exam presents.