PERT / CPM Calculator

How PERT and the Critical Path Method Work

PERT models each activity with three estimates — optimistic (O), most likely (M), and pessimistic (P) — and combines them into an expected duration te = (O + 4M + P) / 6 with variance ((P − O) / 6)². This beta-distribution approximation rewards honest uncertainty ranges instead of single-point guesses.

The critical path method then runs a forward pass (earliest start/finish) and a backward pass (latest start/finish) over the precedence network. Activities with zero total float form the critical path: any delay there delays the whole project, while float on other activities is schedule slack you can consume without moving the end date.

Summing variances along the critical path gives the project variance. With the project duration treated as approximately normal, the z-score (deadline − duration) / σ converts a deadline into a completion probability — a principled answer to "what are the odds we finish by week 20?".

When to Use This Tool

• Planning construction or engineering projects where activity durations are uncertain ranges, not fixed numbers
• Finding which activities actually control the end date before committing crews or expediting fees
• Quantifying schedule risk for a contractual deadline as a probability instead of a gut feeling
• Checking how much float a non-critical activity has before agreeing to delay it
• Re-running the network after a scope change to see whether the critical path moved

Common Mistakes to Avoid

• Entering the same value for O, M, and P — that silently turns PERT into single-point CPM and reports zero schedule risk
• Making the pessimistic estimate a mild "10% worse" — P should reflect a realistic bad case (weather, rework, permit delay), or the variance is meaningless
• Forgetting a precedence link, which shortens the apparent critical path and produces an impossible schedule
• Treating near-critical paths (small float) as safe — a path with 1 day of float is one rain delay away from becoming critical
• Applying the normal-approximation probability to a 3-activity project — the approximation needs a reasonably long critical path to be trustworthy

How to Interpret Results

• Project Duration is the sum of expected durations along the critical path — activities marked ● control the end date
• Total Float per activity is how many time units it can slip without delaying the project; free float (not shown separately here) may be smaller when successors start early
• A completion probability near 50% means the deadline equals the expected finish — commit only with buffer; above ~84% corresponds to one standard deviation of margin
• Large project standard deviation relative to duration signals wide estimate ranges — tighten the riskiest critical activities first
• If several paths have nearly equal length, manage all of them: the reported single critical path can switch with small estimate changes

Related Standards & References

• Malcolm, Roseboom, Clark & Fazar (1959) — Application of a Technique for Research and Development Program Evaluation (Operations Research 7:646-669), the original PERT paper
• Kelley & Walker (1959) — Critical-Path Planning and Scheduling (Eastern Joint Computer Conference), the original CPM formulation
• PMI PMBOK Guide — Schedule Management knowledge area documents PERT three-point estimating and CPM float analysis as standard practice
• AACE International RP 37R-06 — Schedule Levels of Detail, context for applying network scheduling on capital projects

Frequently Asked Questions

Where do the three time estimates come from?

Optimistic assumes everything goes right, most likely is the modal experience-based duration, pessimistic assumes realistic problems (not catastrophes). Use historical data or structured expert judgment, and keep all three on the same calendar basis (working days vs calendar days).

What is the difference between PERT and CPM here?

CPM is the network arithmetic — forward/backward pass, float, critical path. PERT adds the three-point duration model and the probabilistic deadline analysis on top. This tool runs both: deterministic schedule from expected durations, probability from critical-path variance.

Why is my completion probability missing?

The probability is only computed when you enter a deadline. It also requires a non-zero project variance — if every activity has O = M = P, there is no uncertainty to evaluate and the z-score is undefined.