Glossary
PERT Estimate
three-point estimation, three-point estimate, PERT formula, weighted three-point estimate
A PERT estimate calculates the expected duration of an activity from three estimates: optimistic (O), most likely (M) and pessimistic (P). The formula is E = (O + 4M + P) / 6, the standard deviation σ = (P − O) / 6. Example: O = 4, M = 6 and P = 14 days give E = 7 days with σ ≈ 1.7 days.
PERT stands for Program Evaluation and Review Technique. The US Navy developed the method in the late 1950s for the Polaris missile program.1 The PERT estimate is a form of three-point estimation: instead of a single number, you estimate a range and make the uncertainty of an activity visible. The most likely value counts four times, each extreme value once. The weighting assumes a beta distribution.
How do you calculate a PERT estimate?
- Estimate three values. O is the duration if everything goes smoothly. M is the duration you expect most often. P is the duration if known risks occur, but no disaster.
- Calculate the expected value: E = (O + 4M + P) / 6.
- Calculate the standard deviation: σ = (P − O) / 6. The wider the range between O and P, the less certain the estimate.
- State a range. Assuming a normal distribution, the actual duration falls between E − σ and E + σ with a probability of about 68 %, and between E − 2σ and E + 2σ with about 95 %.
Example: PERT estimate for one activity
A team estimates the data migration in an IT project: optimistic 4 days, most likely 6 days, pessimistic 14 days.
| Value | Calculation | Result |
|---|---|---|
| Expected value E | (4 + 4 × 6 + 14) / 6 = 42 / 6 | 7.0 days |
| Standard deviation σ | (14 − 4) / 6 = 10 / 6 | 1.7 days |
| Range E ± σ (about 68 %) | 7 − 1.7 to 7 + 1.7 | 5.3 to 8.7 days |
| Range E ± 2σ (about 95 %) | 7 − 3.3 to 7 + 3.3 | 3.7 to 10.3 days |
The expected value is one day above the most likely value because the pessimistic outlier pulls it up.
How do you apply PERT to several activities?
For a chain of activities on the critical path, add up the expected values. Do not add the standard deviations; add the variances (σ²) and take the square root. This assumes that the activities vary independently of each other.
| Activity | O | M | P | E | σ² |
|---|---|---|---|---|---|
| A Requirements | 3 | 5 | 7 | 5.0 | 0.44 |
| B Data migration | 4 | 6 | 14 | 7.0 | 2.78 |
| C Testing | 2 | 3 | 10 | 4.0 | 1.78 |
| Path | 16.0 | 5.0 |
The standard deviation of the path is √5 ≈ 2.2 days. A deadline at about 18 days (E + σ) holds with a probability of about 84 %. The difference between 16 and 18 days gives you the size of a project buffer.
What is the difference between a PERT estimate and simple three-point estimation?
Simple three-point estimation weights all three values equally: E = (O + M + P) / 3. It equals the mean of a triangular distribution.
| PERT estimate | Simple three-point estimate | |
|---|---|---|
| Formula | (O + 4M + P) / 6 | (O + M + P) / 3 |
| Weight of the most likely value | 4 of 6 | 1 of 3 |
| Example 4, 6, 14 days | 7.0 days | 8.0 days |
| Effect of outliers | damped | strong |
The simple formula reacts more strongly to extreme values and gives the more cautious result for skewed estimates. The PERT formula fits when you trust the most likely value, for example because the team has done a similar activity several times.
Common mistakes with PERT estimates
- Extremes as wishful numbers: O and P describe realistic edge cases, not fantasy figures. A P that can never happen inflates E.
- Adding standard deviations: summing σ instead of σ² overstates the spread of the path.
- Reading E as a safe date: you meet the expected value in only about half of all cases.
- Never re-estimating: update O, M and P as soon as an activity has started and you know more.
How do you use PERT estimates in Merlin Project?
Merlin Project stores one planned duration per activity, but no built-in three-point estimate. Record the three values in custom fields: choose Insert › Column, then For new Field, enter a Field Name such as "Optimistic" and confirm with Insert Column. In the column's Inspector, choose Duration as the Type. Repeat this for "Most likely" and "Pessimistic", then enter the calculated expected value as the activity's duration. Custom fields, the Net Plan and the PERT display are part of Merlin Project, not Merlin Project Express.
The PERT display of the Net Plan shows earliest and latest start, earliest and latest end, expected duration and slack on each card. In Merlin Project, "expected" refers to the plan with actual values taken into account, not to the PERT formula. The guide PERT chart: formula, example and critical path shows how to derive the critical path from the estimates in a network. To calculate a distribution of possible end dates from O and P across all activities, see Monte Carlo simulation in Merlin Project.
