Project Management guide · Scheduling and time
PERT Chart and PERT Estimate: Formula and Worked Example
PERT (Program Evaluation and Review Technique) is a scheduling method that uses three duration estimates for each activity, optimistic, most likely and pessimistic, to calculate an expected duration and a measure of uncertainty. A PERT chart is the network diagram that shows these activities and their dependencies.
Key takeaways
- PERT expected duration = (O + 4M + P) / 6; SD = (P - O) / 6.
- Add expected durations along a path and add variances, not SDs.
- Use the path SD to estimate the chance of meeting a deadline.
- Use PERT for uncertain work and check merges with simulation.
The PERT formulas
| Measure | Formula |
|---|---|
| Expected duration (E) | (O + 4M + P) / 6 |
| Standard deviation (SD) | (P - O) / 6 |
| Variance | SD squared |
| Path SD | Square root of the sum of the variances along the path |
O = optimistic, M = most likely, P = pessimistic. The formula weights the most likely estimate four times as heavily, based on a beta distribution. A simpler alternative, the triangular average (O + M + P) / 3, is sometimes used; see cost estimation.
Worked example: one activity
A design activity is estimated at O = 4 days, M = 6 days and P = 14 days.
- E = (4 + 4 x 6 + 14) / 6 = (4 + 24 + 14) / 6 = 42 / 6 = 7 days.
- SD = (14 - 4) / 6 = 10 / 6 = about 1.67 days.
- Note that the expected duration (7) is longer than the most likely (6) because the pessimistic estimate is far out.
Worked example: a path
| Activity | O | M | P | E | SD | Variance |
|---|---|---|---|---|---|---|
| Design | 4 | 6 | 14 | 7.0 | 1.67 | 2.78 |
| Build | 8 | 10 | 18 | 11.0 | 1.67 | 2.78 |
| Test | 2 | 3 | 10 | 4.0 | 1.33 | 1.78 |
| Path total | 22.0 | 7.33 |
Path SD = square root of 7.33 = about 2.71 days. Assuming the total is roughly normally distributed, there is about a 50% chance of finishing within 22 days, about 84% within 22 + 2.71 = 24.7 days, and about 98% within 22 + 2 x 2.71 = 27.4 days. These figures are approximations; a Monte Carlo simulation gives a more realistic picture when several paths merge.
How to create a PERT chart
- List activities and their dependencies.
- Collect O, M and P estimates from the people doing the work.
- Calculate E and SD for each activity.
- Draw the network diagram using E as the duration.
- Find the critical path with a forward and backward pass.
- Combine variances on the critical path to estimate the probability of meeting the deadline.
- Set contingency or a buffer based on the confidence level the sponsor wants.
PERT vs CPM vs Gantt chart
| PERT | CPM | Gantt chart | |
|---|---|---|---|
| Purpose | Model duration uncertainty | Find the critical path and float | Show the schedule on a calendar |
| Estimates | Three per activity | One per activity | Any |
| Output | Expected duration and probability | Early and late dates | Bars on a timeline |
Limitations and tips
- PERT considers only the critical path and can understate risk where near-critical paths merge.
- Estimates can be biased; ask for the pessimistic case explicitly, not just a padded most likely.
- Use PERT where work is new or uncertain; single estimates are fine for routine work.
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Frequently asked questions
What does PERT stand for?
Program Evaluation and Review Technique.
What is the PERT formula?
Expected duration = (optimistic + 4 x most likely + pessimistic) / 6.
How do you calculate PERT standard deviation?
(Pessimistic - optimistic) / 6.
What is an example of a PERT estimate?
With O = 4, M = 6 and P = 14 days, the PERT estimate is (4 + 24 + 14) / 6 = 7 days.
Why is the most likely value multiplied by 4 in PERT?
The formula approximates a beta distribution in which the most likely value carries the most weight.
What is the difference between PERT and CPM?
PERT uses three estimates to handle uncertainty; CPM uses one estimate and focuses on logic and float.
What is the difference between a PERT chart and a Gantt chart?
A PERT chart is a network of dependencies; a Gantt chart shows activities as bars on a calendar.
What is three-point estimating in PERT?
Estimating with optimistic, most likely and pessimistic values. PERT is one way of combining them; the triangular average is another.
When was PERT developed?
It was developed in the late 1950s for the US Navy's Polaris missile programme.
Is PERT used in Agile?
Not usually in its full form, but three-point thinking is useful for release forecasting alongside story points.