Float and the critical path

What float is

• The float (or slack) of an activity is the spare time it has — how long it could be delayed without pushing out the whole project.
• An activity with float can slip, start late, or run over a little and the project still finishes on time.
• An activity with zero float has no spare time — any delay to it delays the entire project.

Calculating float

• Once both passes are done, float comes straight from the node box:

$\text{float} = \text{LST} - \text{EST} = \text{LFT} - \text{EFT}$

• LST — latest start time (bottom-left). EST — earliest start time (top-left).
• The two forms are equal, so you can use whichever pair is easier — or use one to check the other.
• Float is always zero or positive; a negative float means an arithmetic slip in a pass.

The critical path

• The critical path is the chain of activities from start to finish that all have zero float.
• It is the longest path through the network by total duration — and it sets the project completion time.
• Every project has at least one critical path; there may be more than one if paths tie in length.
• Delaying any critical activity delays the whole project; that is what makes them "critical".

Identifying critical activities

• Work out the float of every activity from $\text{LST} - \text{EST}$.
• Pick out the activities with float $= 0$ — these are the critical activities.
• Join them along the arrows from the first activity to the last: that chain is the critical path.

• In the hall build the critical path is $A \to B \to D \to E \to G$, all with float 0. C has float 5 and F has float 1, so both are non-critical — they have room to slip.