Free Critical Path & PERT Lab

Step 1: PERT 3-Point Estimates & Deadline

Project PERT & Critical Path Configuration

Target Project Deadline (Days)

Used to calculate normal completion probability ($Z$-score) against the critical path variance.

Activity 3-Point PERT Estimating [Optimistic (O), Most Likely (M), Pessimistic (P)]

Activity	Predecessors	Optimistic (O)	Most Likely (M)	Pessimistic (P)
A: Scoping & Charter	None
B: Architecture & Design	A
C: Core Engineering / Build	B
D: Vendor Procurement	B
E: Integration & QA Testing	C, D
F: Deployment & Go-Live	E

Expected Duration

84.0 Days

Total Critical Path Length

Critical Path

Path: A → B → C → E → F

Zero-Float Activities

On-Time Probability

89.2%

Target Deadline Met

Schedule Risk (Z-Score)

Z = 1.24 (σ = ±4.8 d)

Standard Deviation Buffer

Forward & Backward Pass Schedule Matrix

Early/Late Start & Finish dates with Total Float calculation ($TF = LS - ES = LF - EF$).

Activity	Predecessors	Expected ($T_e$)	Early Start ($ES$)	Early Finish ($EF$)	Late Start ($LS$)	Late Finish ($LF$)	Total Float ($TF$)

Operations Research & Project Management

Mastering CPM and PERT Schedulings

The Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) form the bedrock of project management.

Zero Float Is King: Any delay on a zero-float activity cascades directly into delayed project delivery unless fast-tracked or crashed.
Three-Point Weighting: PERT weights the most likely duration $4 imes$ while accounting for asymmetric tail risks.
Project Standard Deviation: Variances sum along the critical path ($sigma^2_{ ext{proj}} = sum sigma_i^2$), providing realistic confidence intervals.

Evaluate process capability in the Process Capability Lab.

CPM & PERT Formulas

Essential schedule risk formulas

PERT Expected Duration Te = (O + 4M + P) ÷ 6

Activity Variance σ² = ((P - O) ÷ 6)²

Total Float (TF) = Late Start (LS) - Early Start (ES) = LF - EF

Project Standard Deviation σ_proj = √(∑ σ²_critical)

Schedule Z-Score = (Deadline - Critical Path Duration) ÷ σ_proj

Balance assembly lines in the Takt Time Lab.

FAQ

Critical Path and PERT questions

What is the Critical Path Method (CPM) in project management?

The Critical Path Method (CPM) is an algorithmic technique for scheduling project activities. The critical path is the longest sequence of dependent activities; any delay in critical path activities directly delays the entire project completion date.

How do you calculate 3-Point PERT expected duration and variance?

PERT Expected Duration Te = (Optimistic + 4 × Most Likely + Pessimistic) ÷ 6. Activity Variance = ((Pessimistic - Optimistic) ÷ 6)^2. Standard deviation is the square root of variance.

What is the difference between Total Float and Free Float?

Total Float (LS - ES or LF - EF) is the total time an activity can be delayed without delaying project completion. Free Float is the time an activity can be delayed without delaying the early start of any immediate successor.

How do you calculate the probability of finishing a project on time?

Z-Score = (Deadline - Critical Path Duration) ÷ Project Standard Deviation. The on-time completion probability is the cumulative normal distribution value Φ(Z).

Can I export Critical Path and PERT schedule matrices to CSV?

Yes. You can export complete activity durations, early/late starts and finishes, total floats, critical path tags, and PERT Z-score probabilities as a UTF-8 CSV spreadsheet with formula injection defense.

Is this tool certified PMP or Primavera scheduling software?

No. This tool provides educational operations and project management simulations for business analysis without certified PMI certification or commercial enterprise ERP scheduling warranties.

Continue Exploring Operations & Quality Tools

Explore our Operations & Quality Hub, benchmark statistical quality in the Process Capability Lab, balance production takt times in the Takt Time Lab, optimize equipment in the OEE Lab, or calculate consulting realization in the Project Profitability Lab.