Last updated October 2026
Three-point estimating replaces a single guess with three numbers: an optimistic value (O), a most likely value (M) and a pessimistic value (P). The PERT formula turns them into one planning figure, E = (O + 4M + P) / 6, with a standard deviation of about (P − O) / 6. The triangular formula uses the plain average, (O + M + P) / 3.
Type your optimistic, most likely and pessimistic values. You get the PERT and triangular estimates, the standard deviation and the value you can be 80% confident of, and a picture of the range the three numbers describe.
There is a 39% chance of coming in at or under the most likely 14 days (29% with the triangular shape), and an 86% chance of coming in at or under your target of 18 days.
Tamara puts ranges like these on every task of a Primavera P6 or Microsoft Project schedule and simulates the whole plan.
The P80 and the chances come from the PERT distribution itself (a beta distribution between O and P), not from a normal approximation, so they can differ a little from calculators that use the estimate plus 0.84 standard deviations.
Turn on JavaScript to use the calculator. The numbers shown are for 10, 14 and 24 days.
With 10, 14 and 24 days, the PERT estimate is 15 days, a day more than the most likely value, and the chance of finishing within 14 days is only 39%. That is the point of the method: a single most likely figure is more likely to be missed than met.
Three-point estimating works for durations and for costs. It is one of the estimating techniques in the PMBOK Guide, and both formulas come up in the PMP exam. For a list of up to 20 tasks, download the free Excel template.
There are two. The triangular formula gives the three values equal weight: E = (O + M + P) / 3. The PERT formula, also called the beta or weighted formula, counts the most likely value four times: E = (O + 4M + P) / 6. For the spread, PERT uses a standard deviation of (P − O) / 6, and the variance is that number squared.
The three formulas, worked for 10, 14 and 24 days
Formula
E = (O + M + P) / 3
Example
(10 + 14 + 24) / 3 = 16.0 days
In short
Each value counts the same.
E = (O + 4M + P) / 6
(10 + 4 × 14 + 24) / 6 = 15.0 days
The most likely value counts four times.
SD = (P − O) / 6
(24 − 10) / 6 = 2.3 days
Variance is SD squared: 5.4.
Both answers sit above the most likely 14 days, because 24 is further from 14 than 10 is. Most tasks look like this. There are more ways to be late than early, so the pessimistic value sits further from the most likely one.
For the PMP exam, learn both formulas and read the question closely. “Simple average” or “triangular distribution” means divide by 3. “Weighted average”, “beta distribution” or “PERT” means divide by 6.
The (P − O) / 6 rule assumes the range covers about six standard deviations, as it would for a normal distribution. It is a handy approximation rather than an exact result: the real standard deviation of the PERT curve for 10, 14 and 24 days is 2.5 days, not 2.3.
Use PERT for most estimates. Both formulas take the same three numbers, but the triangular average gives the pessimistic value as much weight as the most likely one, so one generous pessimistic figure moves the whole estimate. PERT keeps the weight on the most likely value and has a smoother, more natural shape.
Same three numbers, two answers
Optimistic 10, most likely 14 and pessimistic 24 days. The dashed line is the most likely value.
Both shapes start at 10 and end at 24 days. The triangle puts more weight in the long tail, so its estimate and its P80 are higher.
The gap grows with the skew. With 10, 14 and 24 days, the triangle’s estimate is a day higher than PERT’s and its P80 is about a day and a half higher. Neither is wrong. They are two different statements about how often the bad outcomes happen.
In our review of project risk analysis tools we rate both as usable but imperfect. The triangle is easy to understand but tends to overstate the uncertainty. It also leans hard on the maximum, which is the hardest number to know.
PERT, a curvy triangle, is just as easy to understand but tends to understate the uncertainty. The Modified PERT adds a fourth number that sets how sharply the curve peaks at the most likely value, so you can match what the estimator actually believes.
Ask for the pessimistic value first, then the optimistic one, and the most likely value last. Starting from the middle anchors people, and their ranges come out too narrow. Before anyone gives a number, agree what the ends mean: absolute limits, or values with about a one-in-twenty chance of being beaten?
Five steps to a three-point estimate
Name the task, its scope and what is left out. Keep one-off risks, such as a permit objection, out of the range: they get their own chance and impact.
Ask what could make the task run long, and how long it would take then. Talking through the causes stops the number from being a token margin.
Ask what would have to go right, and how short the task could realistically be.
With the range set, ask where inside it the task would most often end up.
Put the three numbers into the calculator above and ask, for example: is there really a one-in-five chance of more than 17 days? Adjust until the estimator agrees, then write down the reasons, their name and the date.
Experts find a true maximum very hard to give. If yours think in percentiles instead, use a distribution built for that. Vose’s software includes a three-point distribution that treats the pessimistic value as a high percentile, such as the 95th, rather than a hard limit.
You can add the expected values: the expected total is the sum of the tasks’ PERT estimates. You cannot add the pessimistic values, the P80s or the standard deviations. And the spread of the total depends on whether the tasks go wrong for the same reasons, which separate estimates do not record.
Take a fence built in ten sections, each estimated at 3, 4 and 6 days with a triangle, as in our review of project risk tools. The most likely values add up to 40 days and the expected total is 43.3 days. What the P80 should be depends on why sections run late.
Ten fence sections, each 3 to 6 days (most likely 4)
Total days for the fence. The dashed line is 40 days, the sum of the most likely values.
Same estimates, two answers: what the total looks like depends on whether the sections go wrong for the same reason. Simulated with 4 million runs.
If each section’s delays are its own, such as a patch of hard ground or a broken post, early and late sections cancel out. The total is narrow: a P80 of 45 days, and only a 4% chance of finishing within the 40 days the most likely values add up to.
If one crew builds all ten sections and its pace drives them all, a slow crew is slow everywhere, and the P80 is 49 days.
Adding up the ten sections’ P80s also gives 49 days (10 × 4.9). That is right only in the second case. Treating tasks as independent when they share a cause makes the total look far more certain than it is. It is the most common way three-point estimates mislead, and it gets worse the more finely a plan is broken down.
In Tamara, one productivity factor for each kind of work moves all the tasks of that kind together, so a slow crew shows up everywhere it works. Try it free for 15 days.
Classic PERT adds up the expected durations along the critical path, adds up their variances, and treats the total as a normal distribution. The chance of finishing by a date is then the normal probability of (date − expected total) ÷ standard deviation. It is quick, but it looks at one path only, so it comes out too optimistic.
Six tasks, two paths that meet at installation
Each task shows its optimistic, most likely and pessimistic days. The darker boxes are the critical path.
Chance of finishing within 100 days
Simulation figures from 2 million runs with PERT distributions.
In this small project, the path through site preparation and foundations is critical. Its expected length is 92.0 days, with a standard deviation of 5.27 (the square root of 6.25 + 6.25 + 6.25 + 6.25 + 2.78). For a 100-day deadline, PERT gives z = (100 − 92) / 5.27 = 1.52, which is a 94% chance.
A Monte Carlo simulation of the same estimates gives 86%. The equipment path is shorter on average, 87.8 days, but far more uncertain, and in 29% of the runs it is the one that finishes last. Whenever either path runs late, so does the project, and PERT’s single-path arithmetic cannot see that. Add a 30% chance of a permit objection on site preparation, and the chance falls to 63%.
PERT was developed in the late 1950s for the US Navy’s Polaris missile programme. Its three-point formula is still the part most people use. For the full picture of a schedule, our guide to Monte Carlo simulation in project management runs this example live, with the S-curve, P50 and P80 dates and a tornado diagram.
Put O, M and P in three columns and use =(B2+4*C2+D2)/6 for the PERT estimate and =(D2-B2)/6 for the standard deviation. To see the range of a total, draw each task from its PERT curve with BETA.INV and RAND(), add the draws up across a row, copy the row down a few thousand times and read off the percentiles.
=(B2+4*C2+D2)/6
=(D2-B2)/6
BETA.INV
RAND()
With O in column B, M in C and P in D, the PERT curve needs two shape values:
=1+4*(C2-B2)/(D2-B2)
=1+4*(D2-C2)/(D2-B2)
=BETA.INV(0.8, F2, G2, B2, D2)
=BETA.INV(RAND(), F2, G2, B2, D2)
The free template does all of this for up to 20 tasks in a row or cost items: the PERT and triangular estimates, each task’s P80, and a 5,000-row simulation of the total with its P50, P80 and P90 next to the sum of the most likely values. It works in Excel 2010 or later with no add-in. Download the three-point estimating template (.xlsx).
A spreadsheet like this has two limits. It adds tasks in sequence, so it cannot show what happens where parallel paths meet. And it draws every task on its own, so tasks that share a cause do not move together. In ModelRisk, the draw is =VosePERT(B2, C2, D2), and our Monte Carlo simulation in Excel guide shows how to correlate items with a copula.
=VosePERT(B2, C2, D2)
Run a Monte Carlo simulation of the schedule instead of adding estimates by hand. And rather than asking for three numbers on every task, describe uncertainty by kind of work and risks by their causes, so that tasks with a shared cause move together, as they do on real projects.
Tamara, our schedule risk software, does this on the schedule you already have.
What Tamara does with a whole schedule
Imports from Primavera P6, Microsoft Project or Microsoft Planner Premium. Your file is never changed.
Define a few uncertainty levels once and give each task a level. Tamara turns them into ranges.
One productivity factor per kind of work moves every task of that kind. Risk events, weather included, get their own chance and impact.
P50 and P80 dates and costs, and a ranked list of what drives them.
Try it on your own schedule with the free 15-day trial. For the method in more detail, see our guide to schedule risk analysis on a Primavera P6 schedule.
Because the weights add up to six: one for the optimistic value, four for the most likely and one for the pessimistic. The 6 in the standard deviation rule has a different source. A range of six standard deviations covers nearly all of a normal distribution.
No. The most likely value is the peak of the curve, and the PERT estimate is its average. When the pessimistic value is further from the most likely than the optimistic one is, the average is higher. That is why the PERT estimate is usually the larger number.
Three-point estimating is the practice of giving three values. PERT (Program Evaluation and Review Technique) is one way to combine them, with the 1-4-1 weighting. It is also the name of the network method the formula came from. The triangular formula is the other common way.
For a single task it is a sensible central figure, but it is met only about half the time (53% for 10, 14 and 24 days). If the date or budget is a commitment, plan to a higher percentile such as the P80. For a whole project, get that P80 from a simulation rather than by adding up task values.
Import your Primavera P6 or Microsoft Project schedule, describe its uncertainty and risks, and commit to dates and budgets at a confidence level you choose.