Understanding the PERT Calculator
PERT stands for Program Evaluation and Review Technique, a project-scheduling method developed by the U.S. Navy in the 1950s for the Polaris missile program. Instead of asking for a single duration guess, PERT asks for three estimates for a task — an optimistic time (if everything goes right), a most likely time (the realistic case), and a pessimistic time (if things go wrong) — and combines them into a single weighted expected duration plus a measure of uncertainty.
The formulas
Given optimistic time O, most likely time M, and pessimistic time P (all in the same unit, with O ≤ M ≤ P), PERT computes:
- Expected time: TE = (O + 4M + P) / 6 — a weighted average that treats M as four times more influential than either extreme.
- Standard deviation: SD = (P − O) / 6 — an approximation from modeling the estimate as a Beta distribution where the full O-to-P range spans roughly six standard deviations.
- Variance: σ² = SD² — used when summing uncertainty across multiple tasks on a project (variances add; standard deviations do not).
- Confidence range: assuming an approximately normal distribution near TE, about 68% of outcomes fall within TE ± 1 SD, and about 95% fall within TE ± 2 SD.
Worked example
Suppose a task has O = 4 days, M = 7 days, and P = 16 days. The expected time is TE = (4 + 4×7 + 16) / 6 = 48 / 6 = 8 days. The standard deviation is SD = (16 − 4) / 6 = 2 days, so the variance is 4 days², and the 95% range is roughly 4 to 12 days (TE ± 2 SD). Notice the expected time (8 days) sits closer to the most likely estimate (7 days) than a plain average of the three numbers (9 days) would — that pull toward M is the whole point of weighting it 4×.
Why not just average the three numbers?
A simple average (O + M + P) / 3 treats every estimate as equally credible, even though the most likely value is presumably the best single guess and the extremes mainly describe the boundaries of what could happen. Weighting M four times as heavily reflects that asymmetry and tends to produce a more realistic central estimate, especially when the pessimistic case is a long tail (common in project work, where things can go wrong in many more ways than they can go unusually well).