PERT, the Program Evaluation and Review Technique, estimates activity duration or cost using three inputs, optimistic, most likely, and pessimistic, with extra weight on the most likely value. PERT was developed for complex programs in the late 1950s and has been widely used since. Wikipedia describes it as a statistical tool for analyzing the tasks in a project, with the expected time computed as (o + 4m + p) ÷ 6.
- Section 1Watch, PERT in 8 Minutes
- Section 2What Is PERT and When To Use It
- Section 3Formulas, Triangular vs PERT
- Section 4Simple Example, Minutes Scenario
- Section 5Advanced Example, Path Uncertainty
- Section 6PERT vs Triangular, Quick Comparison
- Section 7Pros and Cons
- Section 8PMP Exam Relevance
- Section 9PMP Simulator-Style Question
- Section 10Key Takeaways and Next Steps
Watch, PERT in 8 Minutes
Short PrepCast Exam Essentials lesson. Includes triangular distribution and PERT with a quick example.
→ Click here to read the full transcript
Estimators are often overly optimistic. Three-point estimation, in particular PERT, corrects for that by blending optimistic, pessimistic and most likely values into a weighted average that better reflects reality. I'm Cornelius Fichtner and you are watching a PrepCast exam essentials lesson, in which I'll show you exactly how PERT works using two examples taken straight from my PMP training course at pmprepcast.com.
We start by looking at three-point estimations. Here we go, and I'm even wearing the same shirt. Three-point estimating is a simple but very useful approach to estimating the time or cost of work items.
It's also useful here in risk analysis where it allows us and our known risks to be quantified and built into the project budget. In addition, this helps the Monte Carlo simulation, which you just saw, to generate a statistical analysis of the probability of completing the project under budget or within schedule. [Note: This line refers to the full PrepCast course, Monte Carlo is not shown in this standalone video.] And it is called three-point estimation because of the three points that it measures and uses to calculate a result.
It uses the optimistic best case estimate, for example the lowest cost or the shortest duration. And then the most likely estimate. As well as the pessimistic, the worst-case scenario that would be the highest cost, the longest time that an activity may take to complete.
We project managers can use available information from comparable projects or subject matter experts to create these estimates. So three-point estimates can be done in two ways. First, there is the triangular distribution model, which, as the name suggests, calculates a simple average out of three numbers, out of these three numbers that we have here.
Put in a simple format, the equation looks like this. You take the optimistic estimate plus the most likely estimate plus the pessimistic estimate, add it all together, and you divide it by three. That's why it's a triangle, right?
A, B, C, together, divided by three. And then the second one, that is the beta distribution technique. Here, the popular formula that we all use is called PERT, the Program Evaluation and Review Technique.
This uses a weighted average, not just a simple average, to determine the mean of the three estimated values that we have here, plus the pessimistic estimate. Here's the formula. Notice how more weight is given to the most likely scenario.
Optimistic, plus four times most likely, plus pessimistic, and then divided by six. All right. This makes sense because, you know, four times most likely, it's the most likely, right?
See, we want to give that the highest weight. If plotted against the chart, this beta distribution will eventually result in a more uniform bell-shaped curve, which we call the normal distribution. So much for the theory on how to calculate triangular and beta distribution from my PrepCast lesson on risk.
Let's move on to an example. And since these type of estimates, they help you determine how long a task will take in order to develop a schedule, well, the example comes from the lesson on schedule development. Here it is, and I'm still wearing the same shirt, but I'll have to undo this part.
We have talked so much about entering data into the project schedule, which, as we know, is at first always based on estimates. But how do we actually get to a solid estimate? Of course, they are just assumptions, and no one can really predict the future.
But we can definitely see to making our assumptions a bit more stable and correct. One way to do just that is to look at the data. We can calculate how long something could take at its best, worst, and most likely scenario, and then calculate the average of these three values.
This is known as the triangular distribution. In triangular distribution, we need to find the simple average of three estimates to get expected duration. This is called triangular because it's a simple average of our three points.
To calculate the effort, add up our optimistic estimate, the most likely estimate, and our pessimistic estimate, and divide the results by three. For example, we add 28 minutes for our pessimistic estimate, 13 minutes for our most likely estimate, and 10 minutes for our optimistic estimate. The expected duration or effort comes out to be 17 minutes.
Looking at this graph here, I should point out the pattern. The pie chart here is not meant to show different sizes for different estimates, but to show an estimate of effort divided by three. In other words, the triangular distribution assumes that all three estimates weigh equally.
But when they don't weigh equally, another way to calculate weighted average value can be used, called the PERT, or Program Evaluation and Review technique. Here in this technique, the most likely estimate is multiplied by a factor of four. So in essence, we pretend to divide our pie into six slices instead of three.
We then assign one slice to the optimistic, one slice to the pessimistic, and four slices to the most likely estimate. That is exactly what we do with the beta distribution estimate. We weigh or assign more importance to the most likely estimate.
To calculate the effort, we take four times our most likely estimate, add our optimistic estimate and our pessimistic estimate, and then we divide the sum by six. Plugging in the same numbers as before, in this case here, we get an effort of 8.5 minutes.
Note the error on the slide and speech: The correct result is 15 minutes, not 8.5.
The premise, the assumption here is that our estimators, they're simply going to be overly optimistic. The weighted average gives us an estimate of effort that is more balanced and statistically more likely to be accurate. Let's see how the math works in this using different estimates.
In this table, we've plugged in other numbers to see the effect. In the middle of the table, we see both triangular and beta distribution, where estimated time durations came out to be 60 hours. Let's say we had an external optimist on our team.
One estimate she provides says could take as little as 30 hours, another even less at 15 hours. We can see that the triangular distribution is more affected by that lower number, whereas based on beta distribution, the duration estimate stays closer to the most likely estimate of 60 hours. But what if we have a pessimistic estimator?
Overall, our estimate numbers now are larger, but again, our duration estimate, based on the beta distribution, remains closer to the 60 hours, which are our most likely estimate. The wider the range between pessimistic and optimistic value gets, the more statistically significant it is to use the beta distribution formula. And that's it for our PrepCast exam essentials lesson on three-point estimation, in particular triangular distribution and PERT, also known as beta distribution.
Until next time!
What Is PERT and When To Use It
PERT is a three-point estimating technique that applies a weighted average to optimistic (O), most likely (M), and pessimistic (P) estimates for duration or cost. It is especially useful when uncertainty is high or historical data are limited. Here's a quick summary from Wikipedia:
The program evaluation and review technique (PERT) is a statistical tool used in project management, which was designed to analyze and represent the tasks involved in completing a given project.
PERT was introduced by the U.S. Navy Special Projects Office during the Polaris program in the late 1950s, then published in 1958. Its goal was to simplify planning and scheduling for large, complex efforts.
Formulas, Triangular vs PERT
Triangular distribution, simple average
The triangluar distribution is a simple average. Ask your estimators to give you an optimistic, most likely and pessimistic estimate. Add them up. Divide by three:
Expected value = (O + M + P) / 3
PERT (beta approximation), weighted average
We are using the same three estimates as in the formula above, but we give more weight to "most likely". So add up one optimistic, four most likely, and one pessimistic, then divide everything by six:
Expected value = (O + 4M + P) / 6
You also need to know the term "standard deviation", which quantifies the spread of outcomes. In PERT, σ = (P − O) / 6 for an activity, and variances add along a path. A larger σ means greater uncertainty in the estimate.
Spread for path analysis (often used in PERT networks): standard deviation for an activity = (P − O) / 6, and the variance of a path is the sum of variances of activities on that path.
Simple Example, Minutes Scenario
This simple example comes from the video above where Cornelius Fichtner uses the following estimates: O = 10 minutes, M = 13 minutes, P = 28 minutes.
- Triangular, (10 + 13 + 28) / 3 = 51 / 3 = 17 minutes
- PERT, (10 + 4×13 + 28) / 6 = (10 + 52 + 28) / 6 = 90 / 6 =
8.5 minutes15 minutes
Did you notice the calculation error in the video: In the video an “8.5 minutes” result is incorrectly shown. Using the standard PERT formula with O = 10, M = 13, P = 28 gives (10 + 4×13 + 28) / 6 = 90 / 6 = 15 minutes. This is a good PMP habit, always verify with the formula.
Advanced Example, Path Uncertainty
Two activities lie on the critical path. You are given each activity’s duration uncertainty as the range (P − O), with a ±3σ confidence basis:
- Activity 1: P − O = 18 days
- Activity 2: P − O = 24 days
For PERT path analysis, convert each range to a standard deviation first, then add variances along the path:
- σ = (P − O) / 6, so σ₁ = 18/6 = 3 days, σ₂ = 24/6 = 4 days.
- Variance adds along the path: σpath = √(σ₁² + σ₂²) = √(3² + 4²) = √25 = 5 days.
This means there is a roughly 68% probability that the path's total duration will fall within plus or minus 5 days from the expected duration.
Reminder, do not add the ranges directly. Convert to σ first, then sum variances.
Exam tip: The current PMP exam focuses on concepts rather than formulas. It is unlikely you will be asked to calculate a standard deviation. However, you should understand what it represents in PERT: a measure of uncertainty that can be combined along the critical path to assess risk.
PERT vs Triangular, Quick Comparison
- Simple average of O, M, P.
- Treats all three estimates equally.
- Useful for low uncertainty or quick back-of-the-envelope checks.
- Weighted average, (O + 4M + P) / 6.
- Gives more influence to the most likely estimate.
- Better when uncertainty is larger or optimism bias is a concern.
Practical Benefits and Common Pitfalls of PERT
- Easy enough to calculate on the spot. Just three numbers and a formula.
- Forces the team to confront best, worst, and most likely scenarios instead of one guess.
- Reduces optimism bias by weighting the most likely estimate more heavily.
- Reinforces exam understanding of three-point estimating, even if calculations aren’t tested often.
- Provides both an expected value and a measure of uncertainty (σ), useful in schedule risk analysis.
- Getting three credible estimates can be harder than doing the math itself.
- Assumes activity durations are independent, which is often unrealistic on real projects.
- Results depend heavily on the quality of input estimates; garbage in, garbage out.
- Students sometimes confuse triangular (equal weights) with PERT (weighted).
- Doesn’t account for correlation or systemic risks. Monte Carlo simulations handle these better.
PMP Exam Relevance
Today’s PMP exam focuses more on concepts than on manual calculations, but you should still understand how O, M, and P work, when to prefer PERT over a simple average, and how uncertainty aggregates on a path. The conceptual understanding helps with scenario questions and with real project planning.
Here's how PERT might be tested conceptually.
Bias and applicability
The exam might describe a team that consistently underestimates activity durations and ask which estimating technique counters optimism bias. For example: “A project manager notices that her team consistently underestimates activity durations. Which technique should she use?”
Exam focus: Knowing that PERT does not just average numbers. It weights the most likely outcome to reduce optimism bias, making it distinct from triangular or analogous estimating.
Probabilistic thinking for uncertainty
A question could describe an R&D initiative with high uncertainty and ask which advantage makes PERT appropriate. For example: “A project manager is planning an R&D initiative with significant uncertainty in task durations. Which advantage of PERT makes it most useful in this context?”
Exam focus: Understanding that PERT supports probabilistic analysis of activity durations, which helps when variability or risk is high. The focus is on grasping uncertainty, not performing calculations.
PERT vs triangular
You might be asked to distinguish between triangular and PERT in a simple scenario. For example: “Planner A used a simple average of O, M, and P. Planner B gave more weight to the most likely value. What estimating approaches did they use?”
Exam focus: Recognizing that triangular treats O, M, and P equally, while PERT assigns more weight to the most likely estimate. The exam checks if you can tell the difference conceptually rather than crunching numbers.
PMP Exam Sample Question on PERT
A project manager is preparing a schedule using PERT. The sponsor asks whether correlated risks between activities will be reflected in the analysis. What is the best response?
- Yes, PERT inherently accounts for correlation between activities
- No, PERT assumes activity durations are independent
- Yes, but only if you adjust the pessimistic values
- No, PERT replaces the need for sensitivity analysis
→ Click here to reveal answer and explanation
Correct choice: B
General explanation: Classic PERT assumes independence between activity durations. If tasks are correlated, PERT can understate overall risk.
- A. Incorrect. PERT does not model correlation between activities.
- B. Correct. Independence is a simplifying assumption in PERT; correlations require more advanced methods.
- C. Incorrect. Adjusting pessimistic values does not account for correlation.
- D. Incorrect. PERT does not replace sensitivity analysis or Monte Carlo simulation.
A project involves routine, repetitive construction tasks where historical data provides stable single-point estimates. The team suggests using PERT for every activity. What should the project manager do?
- Approve the use of PERT because it always provides more accurate results
- Suggest triangular distribution because it requires fewer estimates
- Recommend simple single-point estimates since uncertainty is low
- Use Monte Carlo simulation for more realistic modeling
→ Click here to reveal answer and explanation
Correct choice: C
General explanation: When activities are routine and uncertainty is minimal, single-point estimates are efficient and reliable. PERT adds overhead without much benefit in such cases.
- A. Incorrect. PERT is not universally “more accurate”; it depends on context.
- B. Incorrect. Triangular still requires three estimates, not fewer.
- C. Correct. Single-point estimates are sufficient when historical data is solid and uncertainty is low.
- D. Incorrect. Monte Carlo is not needed for routine, low-uncertainty work.
Finally, even though we said that the PMP exam doesn't really include PERT calculation questions any longer, here is a sample that does exactly that. Just in case that you want to try your hand at a calculation:
You are estimating an activity with limited historical data. The team proposes O = 8 days, M = 12 days, and P = 26 days. What is the expected duration using PERT, and why?
- 13.7 days, because PERT reduces optimism by weighting the most likely value more heavily.
- 15.3 days, because the triangular distribution gives equal weight to all three estimates.
- 12.0 days, because the most likely value should be used when data are limited.
- 26.0 days, because a conservative estimate minimizes schedule risk.
→ Click here to reveal answer and explanation
Correct choice: A
General explanation: PERT uses a weighted mean that emphasizes the most likely estimate, so (O + 4M + P) / 6 = (8 + 4×12 + 26) / 6 = 82 / 6 ≈ 13.67 days.
- A. Correct. This applies the PERT formula, which weights the most likely estimate four times and yields about 13.67 days.
- B. Incorrect. This is the triangular average, (8 + 12 + 26) / 3 = 15.33 days, which gives equal weight to all three estimates.
- C. Incorrect. Selecting the most likely value alone ignores the spread of outcomes that three-point estimating is designed to capture.
- D. Incorrect. Using the pessimistic value alone is overly conservative and not how PERT or triangular estimates are computed.
Key Takeaways and Next Steps
Here’s what to carry forward into your PMP exam prep and real-world projects:
- Triangular is a simple average. PERT is a weighted average that emphasizes the most likely estimate.
- Standard deviation (σ) = (P − O) / 6. For a path, sum variances and then take the square root.
- Use PERT when uncertainty is high or optimism bias is a risk factor.
- On the PMP exam, expect conceptual questions on PERT rather than calculation drills.
- Download: PMP Formula Study Guide (includes PERT and all key equations).
- Practice: 60 free PMP sample questions in the Exam Simulator.
- Learn more: Watch the full PrepCast course including schedule development for deeper context.
PERT FAQs
Is PERT still on the PMP exam?
Calculations are rare today. Conceptual understanding still appears. Know O, M, P, the PERT mean, and when to prefer PERT over a simple average.
When should I use PERT vs triangular?
Use triangular for quick checks when uncertainty is low. Use PERT when you want a weighted mean that reduces optimism by emphasizing the most likely value.
Is PERT the same as the beta distribution?
PERT uses a beta-based approximation with the mean E = (O + 4M + P) / 6. It is a practical technique that borrows from beta assumptions, not a full statistical fit in every case.
How do I compute standard deviation in PERT?
For an activity, σ = (P − O) / 6. For a path, add variances and take the square root: σpath = √(Σσ²).
Can I use PERT for cost as well as duration?
Yes, the same three-point logic can estimate cost when ranges are credible. Be consistent about how you elicit O, M, and P.
PERT vs CPM in one sentence
PERT uses three-point, probabilistic durations. Critical Path Method (CPM) typically uses single-point, deterministic durations. You can schedule with CPM while sourcing durations from PERT.
What if my activities are correlated?
Classic PERT assumes independence when summing variances. If activities are correlated, the simple variance sum can misstate path risk. Consider Monte Carlo with correlations.
Do I have to use ±3σ when I collect O and P?
No, but be consistent. If O and P reflect a different confidence level, adjust your interpretation. Many teaching examples assume ±3σ for simplicity.
Common pitfalls with PERT
- Treating P − O as σ instead of converting with ÷ 6.
- Mixing triangular and PERT results.
- Ignoring estimator bias when selecting O, M, P.
- Forgetting that path variance adds, not standard deviation.
How does PERT relate to Monte Carlo?
PERT provides a quick analytic mean and σ. Monte Carlo simulates many scenarios using distributions for each activity, which captures nonlinearity and correlations more realistically.
