What the PERT Project Estimator does
This estimator turns optimistic, most likely and pessimistic estimates into a PERT expected duration and standard deviation for each task, adds them up for a sequence of tasks, and gives confidence ranges for the total, the duration you can commit to at a chosen confidence, and the probability of meeting a deadline.
The probabilities use a normal approximation and assume task durations are independent. Both assumptions are stated on the result, because real projects often overrun together.
How to use it
- List each task with three estimates in the same unit: optimistic (things go well), most likely, and pessimistic (things go badly, short of disaster).
- Choose the unit and enter your deadline in it.
- Set the confidence you want to commit at - 80% to 90% is common for external dates.
- Read the expected total, the chance of meeting the deadline and the commitment figure, then check which task contributes most of the uncertainty.
- Download the CSV to keep the estimate with the plan and compare with actuals later.
Reading the results
The expected total is usually longer than the sum of most-likely estimates, because pessimistic tails are longer than optimistic ones. That gap is the optimism a single-point plan hides.
A 50% chance of meeting the deadline means the date is a coin toss. If the date matters, commit at the higher-confidence figure or reduce scope.
The task with the largest share of variance is where learning pays: a spike or prototype that narrows its range shrinks the whole project's uncertainty most.
Worked example: two sequential tasks
Design is estimated at 2, 4 and 8 days: E = (2 + 4 x 4 + 8) / 6 = 4.33, SD = (8 - 2) / 6 = 1. Build is 3, 5 and 13 days: E = (3 + 20 + 13) / 6 = 6, SD = 10 / 6 = 1.67.
Done one after the other, the expected total is 10.33 days. Variances add: 1 + 2.78 = 3.78, so the SD is 1.94 days. The sum of most-likely estimates is only 9 days.
The chance of finishing within 12 days is Phi((12 - 10.33) / 1.94) = Phi(0.86), about 80%. To be 95% confident, commit to 10.33 + 1.645 x 1.94 = 13.5 days.
Formulas and scoring rules
- Expected duration (PERT)
E = (O + 4M + P) / 6- Standard deviation
SD = (P - O) / 6; variance = SD^2- Tasks in sequence
E_total = sum E_i; variance_total = sum SD_i^2; SD_total = sqrt(variance_total)Adding variances assumes independent tasks.- Probability of a deadline
P(total <= D) = Phi((D - E_total) / SD_total)Normal approximation to the sum.- Commitment at confidence q
D_q = E_total + z(q) x SD_total- Central range
E_total +/- z(0.5 + c/2) x SD_totalDurations shown to 1 decimal, SDs to 2.
Limitations: what the result does not prove
- Tasks are treated as one sequence. Work done in parallel, with a critical path that can shift, needs a network model or simulation.
- Independence rarely holds: the same team, the same unknowns and the same late requirements hit several tasks at once, so real risk is usually higher than the formula shows.
- The normal approximation is rough with only a few tasks or very skewed estimates.
- Three-point estimates are only as good as the pessimistic value. People anchor on the most likely figure and set the pessimistic one too close to it.
Privacy: where your data goes
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Standards and sources
Frequently asked questions
What is the PERT formula?
Expected time is optimistic plus four times most likely plus pessimistic, divided by six. The standard deviation is pessimistic minus optimistic, divided by six. Estimates of 2, 4 and 8 days give an expected 4.33 days with a standard deviation of 1 day.
How do I add PERT estimates for several tasks?
For tasks done one after another, add the expected times and add the variances, then take the square root of the total variance for the project standard deviation. Do not add standard deviations directly.
How is a three-point estimate different from PERT?
A simple three-point (triangular) estimate averages the three values equally. PERT weights the most likely value four times, assuming a beta distribution, which pulls the expected value closer to the most likely estimate.
What is the probability of finishing a project by a deadline?
Divide the gap between the deadline and the expected total by the total standard deviation, then read the standard normal probability. The calculator does this and states the independence and normality assumptions behind it.
Why is my PERT estimate longer than my plan?
Because pessimistic outcomes usually overshoot by more than optimistic ones undershoot. The expected value includes that skew, while a plan built from most-likely estimates ignores it.
Can I use hours or weeks instead of days?
Yes. Choose the unit from the menu and use it consistently for every estimate and for the deadline. The calculations are the same in any unit.
Last reviewed by the A2Z.Tools team against the sources listed above.
