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Published September 6, 2026 · By Vincent KENNEL
Critical Path Method: The Calculation, and What Float Means
A schedule can show the same ten days of float on three different tasks. What that figure measures, how the two calculation passes produce it, and where the method came from.
In brief
The critical path is the longest sequence of activities through a project network, and it sets the shortest duration the project can take. Total float is how long an activity can slip without pushing the end date. That float is shared along a path: it does not belong to the activity showing it.
A schedule shows ten days of float on a task. The natural reading is that ten days are available there, and that spending them costs nothing. The number is right. The reading is not, and on a project with committed dates that gap is expensive.
Critical path and float: the definitions
Three objects, and each one answers a different question.
The critical path
The critical path is the sequence of activities that forms the longest path through the network, and it determines the shortest possible duration of the project.
That wording has been stable for over a decade, from the PMI Lexicon of Project Management Terms (2012) through to the PMBOK Guide, 7th Edition (2021), p. 238. The same criterion is used by the GAO Schedule Assessment Guide (GAO-16-89G, 2015), p. 216, and by the NDIA Planning and Scheduling Excellence Guide (PASEG v4.0, 2019), p. 240.
NF ISO 21502:2021, art. 3.8, says the same thing from the other end: the critical path is the sequence of activities that determines the earliest completion date of the project or phase. What determines the earliest finish is what determines the shortest duration.
As long as no date is imposed on the network, that longest path is also the one whose activities carry zero total float. The NDIA PASEG states it directly at p. 135. Once dates are imposed on the network, the relationship between the two criteria becomes a subject of its own, and it is not this article's.
Total float
Total float is the amount of time an activity can be delayed from its early start date without delaying the project finish date or violating a schedule constraint. That is the PMI Lexicon of Project Management Terms wording, carried forward into the PMBOK Guide editions that follow it.
Free float
Free float is the amount of time an activity can be delayed without delaying the early start date of any of its successors, or violating a schedule constraint.
The GAO Schedule Assessment Guide adds the relationship that matters, at p. 217: free float is the portion of an activity's total float that is available before the delay reaches its immediate successor. Free float is not a second definition to learn. It is a part of the first one, and further down it is what the whole argument turns on.
Float and slack
Some authors and some tools call these same two quantities total slack and free slack. Moder, Phillips and Davis, in Project Management with CPM, PERT and Precedence Diagramming, 3rd edition (1983), record that the two sets of names carry identical definitions. Why there are two words at all is a matter of history, and it is taken up at the end of this article.
How they are calculated: the forward pass and the backward pass
Everything above is a result. Two passes over the network produce it.
The forward pass gives the early dates. An activity's early finish is its early start plus its duration, and its early start is the largest early finish among its predecessors. The backward pass gives the late dates, working back from the end of the project: an activity's late start is its late finish minus its duration, and its late finish is the smallest late start among its successors.
The two floats then fall out as subtractions.
Total float is late finish minus early finish, or equivalently late start minus early start.
Free float is the smallest early start among the successors, minus the activity's own early finish.
These are the formulas in Moder, Phillips and Davis, and the GAO Schedule Assessment Guide and the NDIA PASEG (p. 73 and p. 240) carry the same ones.
A small network makes it concrete. Two paths leave the start and reach the finish without meeting. On the upper path, A and B, fifteen days each. On the lower path, D at ten days, then E at five, then F at five.
Task
Duration
ES
EF
LS
LF
Total float
Free float
A
15
0
15
0
15
0
0
B
15
15
30
15
30
0
0
D
10
0
10
10
20
10
0
E
5
10
15
20
25
10
0
F
5
15
20
25
30
10
10
The project takes thirty days. The critical path is A then B, and both carry zero total float.
Three readings come out of that table. D, E and F each show ten days of total float, which is thirty days displayed on a path that can absorb ten days of delay in total. D and E have zero free float, so the part of their displayed float that is theirs alone is nothing at all. And F has free float equal to its total float, because nothing follows it on that path before the project ends.
One word on the counting, because it explains something practitioners run into. The table counts in elapsed working days from zero, with each finish falling at the end of its day, which is the convention Moder, Phillips and Davis use. Other sources count in named calendar days, and their formulas carry plus ones and minus ones as a result. The two families do not contradict each other. They are not counting on the same axis.
One tool note, and no more than that. Microsoft Project computes total float with a formula of its own, the smaller of late finish minus early finish and late start minus early start, and it names the field Total Slack (Microsoft Project documentation, consulted on 4 September 2026).
Float is not a reserve anyone puts into a schedule. It is what the calculation returns, a subtraction between two dates the network produced. Nobody decides it and nobody allocates it.
A deliberately held schedule reserve is a different object, carried elsewhere in the plan and governed by different rules. The GAO Schedule Assessment Guide draws that line at p. 118. Who holds such a reserve, where it sits and who authorises its use are questions for another article.
The float on a task does not belong to it
Total float is calculated against the end of the project, not against the activity. Two activities on the same path therefore display the same number without that number existing twice. In the network above, thirty days are displayed across D, E and F on the non-critical path, and ten days are actually available on it.
Spend float on one activity and it is gone from the ones behind it on the same path.
The same network before and after D consumed five days of the path's float
Four independent sources establish this, two of them decades older than the standards in use today.
John W. Fondahl, in A Non-Computer Approach to the Critical Path Method for the Construction Industry (Stanford Technical Report No. 9, 2nd edition, 1962), is the only one that defines the mechanism rather than asserting it. The share of total float that exceeds free float, he writes, indicates that finishing the operation within that range does not affect project completion but does affect later operations, by reducing their float.
Moder, Phillips and Davis give the most quotable form: activity float is in a sense owned by an individual activity, while path float, or total float, is shared by all the activities along the same float path.
The GAO Schedule Assessment Guide, p. 92 to 97, states that activities on the same network path share total float, and that letting one activity consume it prevents the following ones from slipping.
The PMI Practice Standard for Scheduling, 3rd edition (2019), p. 63 and p. 72, says the value is shared between all the activities on a given path and, symmetrically, that free float is a property of an individual activity. The same standard bounds the sharing at p. 72: it runs to the point where the path merges into another, or to the end of the project.
Which is what gives free float its reason to exist. It is the part of the displayed number that really is the activity's own, and on D and on E that part is zero.
What it is for, on a contract with committed dates
Three uses, on a project whose dates are engaged.
Knowing what drives the finish date, and therefore where effort is worth spending. The critical path is the only place where saving time shortens the project. The NDIA PASEG gives the operational form at p. 137: the sequence of activities tied together by network logic with the longest overall duration between now and program completion.
Knowing what can slip without consequence, and how far. The answer is not the number displayed on the activity. It is what the path still has.
Knowing, before committing to a date, what the path leading to that date still carries. On a contract with intermediate milestones the same logic applies to every committed date: what matters is what drives that particular date, and it is not necessarily what drives the end of the project.
One practice to avoid, from the same PASEG page, in its list of things not to do: total float is not a measurement of variance against the baseline. It is not calculated relative to the baseline position. It is calculated relative to the end of the program.
Where the critical path method came from
Four facts, each read on the source.
There is no birth date. There is a sequence, and a problem to solve. Everything in this paragraph is read on James E. Kelley Jr. and Morgan R. Walker, Critical-Path Planning and Scheduling, in the 1959 Proceedings of the Eastern Joint Computer Conference, p. 160 to 173. In late 1956 the Integrated Engineering Control Group at E. I. du Pont de Nemours opened a study into using electronic computers to master the complexity of engineering projects. That is the problem. The fundamentals of the system were developed in early 1957, and the results of that phase were demonstrated officially in September 1957. A first real trial ran from December 1957 to March 1958. By March 1959, at the Louisville Works, average shutdown duration had come down from 125 hours to 93, and then to 78 once critical jobs were accelerated. That is the operational proof. The paper itself was delivered in December 1959, in Boston.
The letters CPM are not in the founding paper. Kelley and Walker write "the Critical-Path Method", seventeen times, and never the acronym. Inside du Pont the system went by another name, the Project Planning and Scheduling System, as Fondahl records. The expression critical-path is defined in the paper itself, at p. 163: a project that contains critical jobs also contains at least one continuous path of critical jobs from origin to terminus, and such a path is called a critical-path.
Float and slack are two schools, and both are documented. In Kelley and Walker, float is the defined term, and slack appears once, in ordinary non-technical use. On the PERT side, symmetrically, D. G. Malcolm, J. H. Roseboom, C. E. Clark and W. Fazar, in Application of a Technique for Research and Development Program Evaluation, Operations Research vol. 7 (1959), p. 656, define slack as the difference between the latest allowable date and the expected date. The USAF PERT Volume I manual, PERT-Time System Description Manual, in its advance copy of September 1963, uses slack at p. II-6 and does not contain a single occurrence of float. The two vocabularies merged later, which is why the same quantity travels today under two names.
A second foundation, and 1959 is a crowded year. On 20 April 1959 Bernard Roy presented a note to the Académie des sciences, Contribution de la théorie des graphes à l'étude de certains problèmes linéaires, p. 2437 to 2439. The PERT paper was received a week later, on 27 April. The Kelley and Walker paper was delivered in December. Roy's note lays the graph-theoretic ground from which the French vocabulary of potentials descends. What it does not contain bounds what can be said about it: no scheduling term, no float, and no method acronym. It is a mathematical foundation, not a terminological source.
Before committing a date
Before committing to a date, or before letting an activity run late, look at what else sits on the same path. The number displayed on the activity is the path's number.
That is a usable rule at schedule review. A float figure means nothing until you know which path it belongs to, and what else is waiting on that path.
Stop guessing. See the real impact.
Frequently asked questions
Q.Can a project have more than one critical path?
Yes, and on a large network it is common. Two paths of equal length both carry zero total float, so both set the finish date and both have to be watched. Adding a day to either one adds a day to the project.
Q.What does negative float mean?
It means the calculation places the activity behind a date it is required to meet. Total float can be negative; free float cannot. The figure is the amount of time that would have to be recovered for that required date to hold.
Q.Total float or free float, which one should I look at?
Free float, to know whether this activity can slip without moving anything behind it. Total float, to know how far the finish date is from being affected. They answer two different questions, so the useful habit is to display both.
References
AFNOR - NF ISO 21502:2021 - Recommandations sur le management de projet - Juin 2021
Bernard Roy - Contribution de la théorie des graphes à l'étude de certains problèmes linéaires - 1959
DoD - USAF PERT Volume I - PERT-Time System Description Manual - Advance Copy for AFSC Implementation, September 1963
GAO - GAO-16-89G - Schedule Assessment Guide - Best Practices for Project Schedules - 2015
INFORMS - D. G. Malcolm, J. H. Roseboom, C. E. Clark, W. Fazar - Application of a Technique for Research and Development Program Evaluation - vol. 7, no. 5, 1959
James E. Kelley Jr., Morgan R. Walker - Critical-Path Planning and Scheduling - 1959
John W. Fondahl - A Non-Computer Approach to the Critical Path Method for the Construction Industry - 2nd edition, 1962 revision of the original November 1961 report
Joseph J. Moder, Cecil R. Phillips, Edward W. Davis - Project Management with CPM, PERT and Precedence Diagramming - 3rd edition, 1983
Microsoft - Total Slack (task field) - Microsoft Support
