PERT Estimate Calculator Widget
Embed a PERT three-point estimator for project planning. Readers list up to six tasks with optimistic, most likely and pessimistic estimates and get the expected duration and spread of each, plus a total with ranges they can put into a plan.
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How it works
The Program Evaluation and Review Technique was developed for the US Navy's Polaris programme and published by Malcolm, Roseboom, Clark and Fazar in 1959. Each task gets three estimates: optimistic (O), most likely (M) and pessimistic (P). The expected time weights the most likely value four times, (O + 4M + P) / 6, and the standard deviation is a sixth of the range, (P - O) / 6. A design task of 2, 4 and 8 days has an expected 4.33 days and a deviation of 1 day. For tasks done one after another the means add up, but the deviations do not: the variances (squared deviations) add, and the total deviation is their square root. Design plus a 3/5/13 build task gives 10.33 days with a deviation of 1.94, so about 68% of outcomes fall within one deviation (8.39 to 12.28) and about 95% within two (6.45 to 14.22).
Calculation method
- Expected time per task = (O + 4M + P) / 6
- Standard deviation per task = (P - O) / 6; variance = sd squared
- Total mean = sum of means; total sd = sqrt(sum of variances)
- ~68% range = mean +/- 1 sd; ~95% range = mean +/- 2 sd (normal approximation)
Worked examples
Two tasks in sequence
Inputs: Design, 2, 4, 8 and Build, 3, 5, 13 (days)
Result: Expected 10.33 days; sd 1.94; ~68% range 8.39 - 12.28; ~95% range 6.45 - 14.22
Means 4.33 + 6; variances 1 + 2.78.
Three-task default
Inputs: Design 2/4/8, Build 3/5/13, Testing 1/2/4
Result: Expected 12.5 days; sd 2.01; ~95% range 8.49 - 16.51
Testing adds 2.17 days and 0.25 to the variance.
Limitations
- Assumes tasks run one after another and are independent; shared risks make the real spread wider.
- The beta-distribution shortcut and the normal approximation are rough for one or two very skewed tasks.
- Up to six tasks, typed as text lines.
Where publishers use it
- Project-management blogs and PMP exam-prep sites teaching three-point estimating
- Software teams estimating a feature from design to release
- Construction and event planners sizing a schedule with uncertain steps
- Agency proposal pages showing a delivery range rather than one date
- University operations-research and engineering-management course pages
- Research labs and grant applicants estimating experiment and fieldwork phases
Questions
Why weight the most likely estimate by four?
The original PERT method approximates each task with a beta distribution; (O + 4M + P) / 6 is the mean of that approximation. For 2, 4 and 8 days it gives 4.33 rather than the simple average of 4.67.
Why not just add the standard deviations?
Independent uncertainties partly cancel out. Two tasks with deviations of 1 and 1.67 days combine to sqrt(1 + 2.78) = 1.94, not 2.67.
How should I enter the tasks?
One task per line as name, optimistic, most likely, pessimistic - for example Build, 3, 5, 13. The name is optional; the three numbers must be in order O <= M <= P.
What does the 95% range mean?
If the estimates are honest and the tasks independent, about 95 times in 100 the total should land within two deviations of the mean. With 10.33 +/- 3.89 days that is 6.45 to 14.22.
Does it find the critical path?
No. It assumes the tasks run in sequence. For parallel work, run it separately for the longest chain of dependent tasks.
Sources
- Application of a Technique for Research and Development Program Evaluation (Operations Research 7(5): 646-669, 1959) - D. G. Malcolm, J. H. Roseboom, C. E. Clark, W. Fazar - INFORMS; record on RePEc IDEAS . The original PERT paper: activity time estimates from responsible technical people, expressed in probability terms; source of the three-estimate mean and spread used here. Publisher page (doi 10.1287/opre.7.5.646) blocked automated access on 2026-10-01; abstract checked on RePEc.
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