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Three-Point Estimating PMP® Exam Resource

Producing a project estimate for the potential time, effort, and cost required is essential in project planning. One estimating technique suggested by the Project Management Institute in the A Guide to the Project Management Body of Knowledge (PMBOK® Guide) is three-point estimating. This Project Management Academy resource will help you understand three-point estimating and relevant PMP formulas for the PMP exam.

PMP Formula Cheat Sheet

PMP® Exam Formula Cheat Sheet

Learn how to successfully use project management formulas after reading this cheat sheet.

Defining three-point estimating PMP

Three-point estimating, a concept to understand for the PMP exam, can help determine the expected scope, schedule, and costs for a project and its components. As an active PMP credential holder, you are likely to use three-point estimating and other PMP exam formulas when performing processes like Estimating Activity Durations and Estimating Costs.

At the start of a project, you may have limited information to help you produce a project estimate. First, you will need to break a project down into a list of estimable tasks, also known by Project Managers as the  Work Breakdown Structure (WBS), and then you or the team member assigned to each task will need to estimate how long or how much money each task will require.

PMP credential holders use three-point estimating to look at three values, or points, to establish an overall estimate for the cost or time of a project and its components:

  • Optimistic estimate (O): in the best-case scenario, what is the least amount of time or money a project or activity would need?
  • Most likely estimate (M): if you were to complete a project or activity 100 times, what is the average amount of time or money you would need?
  • Least likely estimate (L): in the worst-case scenario, if everything somehow goes wrong, how much time or money would a project or activity need?

Although the optimistic estimate and the least likely or “pessimistic” estimate represent extreme options, the estimates themselves should be somewhat realistic. Likewise, in three-point estimating, the most likely estimate represents the expected outcome; it is not just the average of the other two estimates.

You would then combine these values using the three-point estimating formulas for a full probability distribution or for estimating other variables and potential situations.

Three-point estimating PMP exam tips

It’s necessary to understand when, why, and how to use three-point estimating for the PMP exam. You should know the various three-point estimating formulas and aspects of Estimating Costs and Schedules and what scenarios might require them.

Three-point estimate formula PMP

There are two approaches to three-point estimating you should know. Each approach uses an estimating formula that places a different weight on the three estimated points: optimistic (O), most likely (M), and least likely (L).

The triangular distribution is also known as a simple average. This form of three-point estimating is based on the average of each of the three estimated values. Simply add O+M+L and divide by six to get your three-point estimate (E).

Triangular Distribution is a form of three-point estimating

The PERT approach, or Program Evaluation and Review Technique, is also known as a beta distribution or weighted average. This three-point estimating formula gives more weight to the most likely estimate (M). You would use the following formula to get the three-point estimate (E):

Three-Point Estimation Formula PMP

After estimating each task using these three-point estimating formulas, the next step is to estimate the total value for the project. This formula is relatively simple: add together the estimates for each task in a project to get the total sum estimate for the project. Here’s the formula:

Total Value for Project

In the above formula, E(project) represents the total estimated value for the project, and ∑E(task) represents the sum of all task estimates.

Next, use the formula below to calculate the standard deviation (SD) of the estimate for each task time.

Standard Deviation PMP

After using this formula to calculate the standard deviation for each task, or SD(task), the next step is to calculate the total standard deviation for the project, or SD(project). This step uses the following formula:

Total Standard Deviation for the Project will help ensure your three point estimating values are within a specified range.

Standard deviation (SD) is used to calculate confidence levels in the accuracy of a cost or schedule estimate to help ensure your three-point estimating values are within a specified range of accuracy. You can convert estimates into confidence levels + or – a specified sigma of standard deviation as follows:

  • Estimate (E) plus or minus one sigma (1 x SD) equals 68% level of confidence
  • E +/- 2 sigma = 95% confidence level
  • E +/- 3 sigma = 99.7% confidence level

Typically, the 95% confidence level is used in project estimating.

Here’s a summary of all the steps an active PMP credential holder might use when relaying on three-point estimating:

  1. Determine the WBS.
  2. Define three points for each task: optimistic (O), most likely (M), and least likely (L).
  3. Calculate the estimate for each task using either triangular distribution or PERT formulas.
    1. Calculate the total estimate for the project with the E(project) PMP formula.
  4. Calculate the standard deviation of each task using the provided PMP formula.
    1. Calculate the total standard deviation of the project with the SD(project) formula.
  5. Convert the project estimate to confidence levels.

Three-point estimating PMP exam sample questions

You could be asked to use the appropriate formula to calculate a simple three-point estimating PERT or triangular distribution example on the PMP exam when given all the examples. You may even be asked to determine what number of sigma an estimate is accurate to based on a percentage given in the text of a question on the PMP exam.

Ready to put your 3-point estimate PMP knowledge to the test? Try out these PMP exam practice questions and check your answers at the bottom of the page.

Estimates to complete one of your project activities have been submitted to you from experts on your project team. The estimates are as follows: The pessimistic estimate is 126 days, the optimistic estimate is 108 days, and the most likely estimate is 114 days. Using the traditional, beta distribution PERT formula, you can say with 68 percent certainty that the project will finish within which range of dates?112 days to 118 days111 days to 117 days114 days to 116 days113 days to 115 days
Assuming a PERT weighted average computation, what is the probability of completing the project within plus or minus 3 standard deviations of the mean?68.26%99.73%95.44%75.00%
Answers are located at the bottom of the page.

Studying for the PMP Exam?


Three-point estimating helps active PMP credential holders generate project estimates and calculate the accuracy of those estimates within an acceptable range. Quantifying these concepts is crucial in estimating a project’s scope, schedule, and costs, as well as reporting to project stakeholders.

Was this guide to three-point estimating helpful? Do you have any further questions about the PMP exam? Your Project Management Academy experts are here to help. Get in touch with us anytime to stay on the path to PMP success.

Answers to sample questions

  1. A. First, you must determine expected value using the beta distribution PERT formula. That formula is:(Optimistic + Pessimistic + (4 x Most Likely)) / 6. The formula solved for this question is:(108 + 126 + (4 x 114)) / 6 = 115. Next, you need to determine the standard deviation. Standard deviation is calculated as: (Pessimistic – Optimistic) / 6. The standard deviation formula for this question is: (126 – 108) / 6 = 3. The 68 percent confidence level is determined by adding and subtracting one standard deviation to the expected value. Therefore, the range of dates for this question is 112 days to 118 days.
  2. B. Applying normal probability analysis (bell curve), the work will finish within plus or minus 3 standard deviations (SD) 99.73% of time. Work will finish within plus or minus 2 SD’s 95.44% of the time. Work will finish within plus or minus 1 SD 68.26% of the time. With each SD you add you are making the range wider so that the probability of completing the work in that time frame becomes higher.

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Erin Aldridge, PMP, PMI-ACP, & CSPO
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Erin Aldridge, PMP, PMI-ACP, & CSPO