Simple Formula Questions Part 1 – Three Point Estimates

By Vinai Prakash

First of all, thanks to all of you who took part in the mini survey, and helped me assess in what way can I help you to prepare for the PMP exam. If you haven’t done it yet, appreciate if you could take a minute, and take the survey at

Many Formula Questions on the PMP Exam

Many PMP aspirants dread the formula questions on the PMP exam. Most of the formula questions come from the area of Cost Management & Time Management, generally using the Earned Value Mangement techniques.

However, there is a group of very simple formulas, which once mastered, can easily yield many right answers on the PMP Exam.

Such simple forumals belong in the Cost, Communication and Quality Management areas. I’ll divide this post into multiple parts, focusing on 1 simple formula at a time. This one focuses on the Three Point Estimation Technique.

1. Three Point Estimate:
The 3 point estimate belongs to the time management knowledge area. It can also be used during Cost Estimation.

A three point estimate is a better estimate, compared to a single point estimate. Single point estimate simply gives you a single number – for example,

Manager: How long will it take to complete the engine design?

Engineer: 5 days.

The problem with single point estimates is that they are seldom correct.

How reliable is this 5 days estimate? It will depend on the engineer, and whether this task has been done before or not? If it is a routine task, and has been performed many times, a single point estimate may be ok…

But if it is something never done, or is a new activity, or the engineer is new to this activety, this number may well be incorrect. In such cases, going for a three point estimate will give you more reliability.

Three point estimate looks at the most optimistic estimate (O), a most likely estimate (M), and a pessimistic estimate (Least likely estimate) or (L).

In simple terms, let’s take the same question, and ask the engineer again, as follow:

Manager: Usually how long does it take to complete the engine design?

Engineer: About 5 days.

Manager: Great. And what if there were problems… unexpected issues come up, and there are new things that we haven’t thought up of arise?

Engineer: Well, in that case, it might take as long as 10 days, worst case!

Manager: I see. And how about if everything goes smoothly. No hiccups, and no problems? What’s the best case?

Engineer: Then I could get it done in just 3 days flat.

So the manager could then take a simple average, and get the three point estimate as:Online PMP Training

Three Point Estimate = (O + M + L) / 3

E = (5 + 10 + 3) / 3 = 18/3 = 6 Days.

Or the mangaer could add some weightings to the estimated. Like employing PERT (Program Evaluation and Review Technique). This gives you a better estimate.

A commonly used weighting might be – there is less chance of the worst case or the best case happening. In good faith, most likely estimate (M), is what it will take to get the job done. So with this, the three point weighted average estimate would be:

Three Point Estimate = (O + 4M + L ) / 6

E = (3 + 4*5 + 10) / 6 = (3 + 20 + 10) / 6 = 33/6 = 5.6 Days.

This three point weighted average estimate is a much better technique. Use it first, if all the 3 estimates are given.

So when do you use teh Simple Average 3 point estimate? Only when the question explicitely say – using the Tringular Distribution method.

PMP Mock Exam Question on Three Point Estimate:

Q1: Moon Travels are planning on implementing a travel booking system. In the past they were using a completely manual system, which caused errors and delays for their customers. The project manager is confident that the implementation will be completed in 6 weeks, with a most optimistic estimate being 4 weeks, and the worst case scenario might take it to 11 weeks. What must be the three point estimate for this travel booking system implementation?

A: 4 weeks
B: 6 weeks
C: 11 weeks
D: None of the Above.

Doing the calculations, you can arrive at
E = ( 4 + 4*6 + 11) / 6
E = (4 + 24 + 11) / 6 = 39 / 6 = 6.5 weeks.

So the current answer would be D.

Q2: You are the project manager of Libra Travels SSS Project.  You have decided to use the 3 point estimation technique for his project. For the “Test Corporate Bookings” activity, the following estimates are available. O=4, P=9, M=5. What is the result of this estimate?

A: 5.5 weeks
B: Eighteen weeks
C: 33.33 Days
D: Three weeks

Doing the calculations, you can arrive at
E = ( 4 + 4*5 + 9) / 6
E = (4 + 20 +9) / 6 = 33 / 6 = 5.5 weeks.

So the current answer would be A.

Hope this helps you in understanding this simple formula for the PMP Exam.

In the next post, I’ll touch up on another one of the simpler formulas for the PMP Exam.

Post any comments or feedback.


Vinai, PMP


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4 thoughts on “Simple Formula Questions Part 1 – Three Point Estimates”

  1. how do you know if you are to divide by 3 or 6? three point is 3 but if you are using PERT then it should be 6, right? or should I always do both and see which answer is in the list or choices?



    • Most of the time use PERT technique for estimation, PMI expects this estimation because this is more accurate than simple average.

  2. Hello

    I am trying figure out why I keep coming up with the wrong answer to the questions below. I am using the Three Point Estimate and keep getting 9 the book answer is 8. Am I reading the questions wrong? Please see question below. Thanks Mark

    The PERT estimate is nine hours. The best-case estimate is four hours and the worst-case estimate is 18 hours. What is the most-likely duration estimate:
    a. 11 hours
    b. 9 hours
    c. 8 hours
    d. 5 hours

    • Mark, this question can be answered if you know the formula for PERT.
      PERT = ( Optimistic + Pessimistic + 4 times Most Likely ) / 6
      9 = ( 4 + 18 + 4 x ) / 6
      54 = 22 + 4x
      4x = 54 – 22 = 32
      x = 8
      Hope this helps – Vinai


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