Estimate project completion date using three-point estimation with probability distribution and confidence interval charts.
Three-point estimation turns three guesses per task into a completion date with a defensible range. You enter an optimistic, most likely, and pessimistic duration for each task; the tool combines them into an expected total, projects the completion date, and draws the probability distribution with confidence bands such as 68% and 95%. The thing most users are surprised by: the headline date is not your most likely date. The expected value is a weighted average, and because pessimistic ranges usually stretch farther than optimistic ones, the projected date lands later than your middle guess, with a wider band than intuition suggests.
A concrete input and expected output from the current implementation.
Input
Task 1: optimistic 5, most likely 8, pessimistic 14 (working days). Task 2: optimistic 3, most likely 5, pessimistic 9 (working days).
Expected output
Expected total: 13.83 working days, standard deviation 1.80 days. The projected date is your start date plus 13.83 working days. Confidence bands: 68% from 12.0 to 15.6 days, 90% from 10.9 to 16.8 days, 95% from 10.3 to 17.4 days. Probability of finishing on or before the projected date: about 50%.
Each task's expected duration is (O + 4M + P)/6: (5 + 32 + 14)/6 = 8.50 and (3 + 20 + 9)/6 = 5.33, summing to 13.83. Each task's standard deviation is (P - O)/6: 1.50 and 1.00, and variances add: 2.25 + 1.00 = 3.25, so the total standard deviation is sqrt(3.25) = 1.80. The 95% band is 13.83 +/- 1.96 x 1.80, rounding to 10.3 to 17.4 days.
For each task, expected duration is (O + 4M + P)/6 and standard deviation is (P - O)/6. The weighted average leans on the most likely value, while the spread depends only on the gap between the optimistic and pessimistic figures: a wide O-to-P range widens the confidence bands, a narrow one tightens them. These are the classic three-point formulas from the PERT technique.
Expected durations add directly to give the total; variances (standard deviation squared) also add, assuming tasks are independent and sequential. The total is then treated as approximately normal - reasonable once several tasks are summed - so about 68% of outcomes fall within one standard deviation of the expected date and 95% within roughly two. The chart plots this curve and marks the completion-date bands you asked for.
Because the formula reports the mean, not the middle of your range: (O + 4M + P)/6 shifts toward whichever of O or P is farther from M. Pessimistic estimates usually stretch farther, so the mean lands right of your most likely guess. Under the normal model, that mean is the 50% point: finishing by it and finishing after it are equally likely.
Under the tool's assumptions, if the project were repeated many times with the same estimates, the completion date would land inside the band about 95 times out of 100. It is not a guarantee: it covers only the uncertainty you typed in. Forgot a task, changed scope, or optimistic inputs, and the true probability of finishing inside the band drops below 95%.
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