How this calculator works
The three-point estimate is a weighted average that puts most of the weight on the most likely duration. The optimistic and pessimistic values each count once, and the most likely counts four times, so the expected time is (optimistic + 4 x most likely + pessimistic) / 6. The spread between the optimistic and pessimistic values becomes the standard deviation, divided by six because that range is treated as roughly six standard deviations across a normal distribution. The z-score measures how many standard deviations the deadline sits above the expected time, and the normal distribution converts that into a probability. The percentile table gives the duration you would quote for a chosen confidence level, which is often more useful for planning than a single expected value.
Formula
expected = (optimistic + 4 x most likely + pessimistic) / 6. standard deviation = (pessimistic - optimistic) / 6. z = (desired time - expected) / standard deviation. probability = the standard normal cumulative distribution at z. Duration at a confidence level = expected + z x standard deviation, with z equal to 0, 0.8416, 1.2816 and 1.6449 for 50, 80, 90 and 95 percent.
Worked example
Optimistic 4 hours, most likely 6 hours and pessimistic 8 hours give an expected time of (4 + 24 + 8) / 6 = 6 hours and a standard deviation of (8 - 4) / 6 = 0.667 hours. An 8 hour deadline is three standard deviations above the mean, so the chance of finishing by then is 99.87 percent. A 90 percent estimate is 6 + 1.2816 x 0.667 = 6.85 hours.
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Frequently asked questions
Why does the most likely estimate count four times?
The weighting comes from the original PERT work and approximates a beta distribution for activity duration. It makes the expected time close to the most likely value while still pulling toward the optimistic and pessimistic ends. The exact weights are a modelling choice, not a law of nature.
What if my three estimates are far apart?
A wide optimistic to pessimistic range produces a large standard deviation, which widens every confidence interval. That is useful information: the task is uncertain. If the range is wide because the work is poorly understood, try to break the task into smaller pieces with tighter estimates rather than trusting a single wide distribution.
Can the probability be below zero or above one?
No. The normal distribution is defined everywhere, and its cumulative probability stays between 0 and 1. A very early deadline gives a probability close to 0, and a very late one approaches 1. The z-score itself can be any real number.
Does PERT require a normal distribution?
The basic method assumes a beta distribution for each activity and uses the normal distribution for the project total by the central limit theorem. For one activity the normal approximation is a convenience. If the optimistic and pessimistic values are very asymmetric, the normal model can misstate the tails, so treat the probabilities as estimates.