Hong Life CalculatorsUnderstanding the PERT calculator — concept and principle
This calculator applies the PERT three-point estimate to a chain of tasks. For each task you enter an optimistic, most likely and pessimistic duration; it returns the expected total duration, its standard deviation, the chance of finishing by a deadline, and the durations you can promise with 90% and 95% confidence. Project managers use it for schedule risk on the critical path.
How it is calculated
- Expected time per task te = (o + 4m + p) ÷ 6
- Standard deviation per task σ = (p − o) ÷ 6
- Path total: Σte; path standard deviation = √(Σσ²)
- Chance of finishing by deadline T = Φ((T − Σte) ÷ √Σσ²), using the normal distribution
- 90% duration = Σte + 1.2816σ; 95% duration = Σte + 1.6449σ
Enter each task on its own line: name, optimistic, most likely, pessimistic.
The principle
PERT was developed in the late 1950s for the US Navy's Polaris programme and published by Malcolm, Roseboom, Clark and Fazar in 1959. It treats each task's duration as uncertain and approximates it with a beta distribution, giving the weighted mean (o + 4m + p) ÷ 6 that leans toward the most likely value. For tasks done one after another, expected times add, and, if the tasks are independent, so do their variances. By the central limit theorem the total is roughly normal, which lets you turn a deadline into a probability.
Worked example
Defaults: Design 3/5/9, Build 8/12/20, Test 2/4/8, Launch 1/2/4; deadline 26.
- Expected times: 5.33, 12.67, 4.33, 2.17; total = 24.5; longest task = 12.7 (Build); 4 tasks.
- σ per task: 1, 2, 1, 0.5; variance sum = 1 + 4 + 1 + 0.25 = 6.25; σ = 2.5.
- z = (26 − 24.5) ÷ 2.5 = 0.6; chance = Φ(0.6) = 72.6%.
- 90% duration = 24.5 + 1.2816 × 2.5 = 27.7; 95% = 24.5 + 1.6449 × 2.5 = 28.6.
How to read the result
A 72.6% chance means roughly one project in four like this would miss the 26-day deadline. If you need more certainty, quote 28 or 29 days, or reduce risk on the task with the largest spread, here Build. Enter only tasks on the critical path; parallel paths that could also become critical make the real chance lower.
Common mistakes
- Giving a narrow range for tasks you have never done before.
- Adding tasks that run in parallel as if they were in sequence.
- Assuming tasks are independent when one delay causes another.
- Treating the probability as exact.
Frequently asked questions
Why is the most likely value weighted by 4?
It comes from the beta-distribution approximation PERT uses, which places most weight on the most likely estimate.
What is the difference between PERT and the critical path method?
The critical path method uses single durations; PERT adds three-point estimates to model uncertainty.
How do I raise my chance of meeting the deadline?
Shorten or de-risk the tasks with the largest spread, or negotiate a later deadline.
Sources: D. G. Malcolm, J. H. Roseboom, C. E. Clark and W. Fazar, "Application of a Technique for Research and Development Program Evaluation", Operations Research 7(5):646–669 (1959) · NPTEL (IIT), "Project and Production Management", Module 2: Project Planning (S. G. Deshmukh, A. Kanda)