three point estimation

Today, we will discuss the three-point estimation technique in project management.

Three-point estimating is a quantitative assessment technique that uses a mathematical process to calculate estimation. 

Workflow cost and schedule estimation are crucial for project managers. The three-point estimation technique offers an effective method to balance timelines, prepare for uncertainties, and interpret estimate disparity. 

Let’s get started.

Three-Point Estimation

Three-point estimation is a cost and schedule estimation technique that reduces biases or uncertainties while appraising activity cost or duration.

Instead of relying on just one estimate, three are computed for each task and averaged to reduce uncertainties, risks, and biases. The estimation derived from the three-point approach is more accurate than analogous and parametric estimation.

Two types of three-point estimates provide helpful guidance: triangular distribution and beta distribution (PERT).

Triangular Estimation

  • This technique predicts cost or duration by applying an average of Optimistic, Pessimistic, and Most Likely estimates. These methods are sometimes described as an independent subcategory of estimation techniques.
  • Triangular distribution will be represented by this formula: E = (O+ML+P)/3 where E = Estimate, O = Optimistic, ML = Most Likely, and P = Pessimistic.
  • In this technique, each estimate has an equal weight. Thus, the Most Likely estimation does not influence the final assessment more than twice the Less Likely estimates. 

Optimism and Pessimism in Estimates

Creating realistic estimates poses a challenge because optimism and pessimism are inherent in human nature and can lead to bias and imprecise estimates. 

Many reasons cause optimism and pessimism: experience, personal and business interests, stakeholder expectations, management pressure, constraints, ethical issues, and organizational culture.

The Program Evaluation and Review Technique (PERT)

  • The Program Evaluation and Review Technique (PERT) is a sophisticated form of the range-estimation technique; simply calculate the cost or duration estimate by applying a weighted average of Optimistic, Pessimistic, and Most Likely estimates.
  • PERT weights the Most Likely data by four times its value to reinforce its significance. The PERT formula is E = (O + 4ML + P)/6, which results in a beta distribution formula.
  • To reduce estimate inflation, historical data can be used to adjust the predictions.
  • A weighted average of the estimate range provides a more valuable forecast than a single Most Likely calculation. Project estimators tend to be overly optimistic, so using the PERT formula can produce a more statistically accurate result.

Examples of Three-Point Estimation

A project manager offers a Most Likely estimate of 100,000 USD for developing a new Graphical User Interface in the software, hypothesizing that, depending upon the materialization of identified project risks, the final cost could be anywhere between 66,000 USD and 210,000 USD. 

Using the PERT formula, 

where O = 66,000 USD, 

P = 210,000 USD, 

and ML = 100,000 USD, 

The PERT estimate would be = (66,000+4*100,000+210,000)/6

= 113,000 USD

Using Triangular Distribution (explained below), the project will cost between 41,000 USD and 185,000 USD with a 99.7% probability. 

Note that the range is high because of the substantial deviation between Optimistic and Pessimistic costs estimated.

Triangular vs Beta Distribution and their Probabilities

To compare estimates for a typical work package, consider the numbers below:

  • Optimistic estimate (O): 15 days
  • Most Likely estimate (ML): 24 days
  • Pessimistic estimate (P): 30 days

Using Triangular Distribution, the work package will need: (O+ML+P)/3 = (15+24+30)/3= 23 days.

Using Beta Distribution, it will need: (O+4*ML+P)/6 = (15+4*24+30)/6= 23.5 days.

In beta distribution, the estimated effort is greater than in triangular distribution because no element has equal weight and Most Likely has more weight than others.

Let’s calculate standard deviation between estimates: (P-O)/6 = (30-15)/6 = 2.5 days.

PERT reveals the 3-Sigma standard deviation has a high probability of occurrence with 99.7% probability, whereas 1-Sigma standard deviation will occur with a probability of 68.3% and 2-Sigma standard deviation with a probability of 95.5%.

To calculate boundaries of estimates based on standard deviation, the formulae used are:

Lower Boundary = Beta Estimate – (# of times of standard deviation)

Upper Boundary = Beta Estimate + (# of times of standard deviation)

For 3-Sigma standard deviation,

Lower Boundary = 23.5 – 3*2.5 = 16

Upper Boundary = 23.5 + 3*2.5 = 31

Sound estimations are usually measured in the range rather than a specific number. 

Using PERT Beta Distribution, with 99.7% probability, the project’s duration will be between 16 and 31 days.

This technique is particularly useful, especially if there is a wider range between optimistic and pessimistic estimation values.

If we want to complete the project within exactly 23.5 days, the probability of meeting this completion time is approximately 15.9%.

When project team members calculate task length, they often add extra time as a buffer to cover risks. The resulting inflated schedule squanders time and money. Reducing the buffer can develop a realistic schedule, unaffected by bias. 


Developing a schedule and cost baseline requires accurate estimation; however,  many projects lack historical data to compare the results. In such cases, three-point estimation, which factors standard deviation, allows project managers to predict workflow effectively. 

Estimations are approximate, so choose the appropriate technique according to circumstances. If you need a reasonably accurate result within a feasible period, three-point estimating provides a valuable advantage. 

Please note that, if you are preparing for the PMP certification exam, this is an important topic and you may see a few questions in the exam from this three-point estimation technique.

How are you using three-point estimation in your project? Please share your experience with this cost-estimating technique.