A PERT chart is a network diagram that shows activities as nodes, dependencies as arrows and, for every activity, an expected duration based on three estimates: te = (o + 4m + p) / 6. The US Navy Special Projects Office introduced the Program Evaluation and Review Technique in 1958 for the Polaris missile program. Our example works through an office refit with 7 activities and a result of 29 working days.
What Is a PERT Chart?
A PERT chart is a network diagram that links all activities of a project, their dependencies and their expected durations in one graphic. From it you read the critical path, the chain of activities that determines the project end, and the float or slack of every other activity.
PERT stands for Program Evaluation and Review Technique. The US Navy Special Projects Office developed the method with Booz Allen Hamilton and Lockheed for the Polaris program and published it in 1958 (sources: Wikipedia, Program evaluation and review technique; Mosaic Projects, White Paper WP1087). At about the same time, DuPont developed the Critical Path Method (CPM). The difference: CPM works with one fixed duration per activity, PERT with three estimates and therefore with uncertainty.
What Is a PERT Chart Used For?
- Completeness: Drawing the network forces you to think through the entire project. Missing activities stand out.
- Sequence: The chart shows which activity waits for which.
- Bottlenecks: The critical path shows which activities you need to monitor closely.
- Schedule risk: The spread of the estimates tells you how likely a deadline holds.
- Communication: Stakeholders see on one page why the project takes as long as it does.
Tip: The Merlin Project learning path explains traditional, agile and creative project management step by step.
How Do You Calculate the Duration with PERT?
The PERT duration is a weighted average of three estimates: te = (o + 4m + p) / 6. The most likely value counts four times, each extreme value once. The standard deviation σ = (p − o) / 6 describes how far the actual duration can spread around te.
The three values of a PERT estimate mean:
- Optimistic (o): duration if everything goes smoothly.
- Most likely (m): duration under normal conditions.
- Pessimistic (p): duration if the foreseeable obstacles occur.
te = (o + 4m + p) / 6σ = (p − o) / 6
Example for a single activity: A prototype takes 5 days in the optimistic case, 8 days in the most likely case and 14 days in the pessimistic case.
te = (5 + 4 × 8 + 14) / 6 = 51 / 6 = 8.5 daysσ = (14 − 5) / 6 = 1.5 days
So plan 8.5 days, not the 8 days of the most likely value. The asymmetry of the estimate adds the extra half day: the pessimistic value lies 6 days above m, the optimistic value only 3 days below.
PERT Chart Example: What Does a Network with a Critical Path Look Like?
A PERT network links the expected durations of all activities through their dependencies to one overall date. Our example: an office is refitted and then occupied. Seven activities, three estimates each in working days, all values checked in Python.
| Activity | Predecessor | o | m | p | te | σ | Earliest start | Latest start | Slack |
|---|---|---|---|---|---|---|---|---|---|
| A Survey and planning | none | 3 | 5 | 13 | 6.0 | 1.67 | 0 | 0 | 0 |
| B Order furniture and network hardware | A | 10 | 15 | 26 | 16.0 | 2.67 | 6 | 7 | 1 |
| C Remove interior walls | A | 2 | 3 | 4 | 3.0 | 0.33 | 6 | 6 | 0 |
| D Install electrics and network cabling | C | 4 | 6 | 14 | 7.0 | 1.67 | 9 | 9 | 0 |
| E Painting and flooring | D | 5 | 7 | 9 | 7.0 | 0.67 | 16 | 16 | 0 |
| F Assemble furniture and hardware | B, E | 2 | 4 | 6 | 4.0 | 0.67 | 23 | 23 | 0 |
| G Move-in and acceptance | F | 1 | 2 | 3 | 2.0 | 0.33 | 27 | 27 | 0 |
PERT chart: office refit with 7 activities
Expected duration te in working days, earliest start and earliest finish counted from project day 0
Our own worked example. All values calculated with te = (o + 4m + p) / 6.
How to read the result:
- Forward pass: Every activity starts as soon as its last predecessor finishes. F waits for B (finish day 22) and E (finish day 23) and therefore starts on day 23.
- Project duration: G finishes on day 29. The expected duration is 29 working days.
- Critical path: The chain A, C, D, E, F, G has no slack. Every day of delay on one of these activities postpones the move.
- Slack: Ordering (B) may start one day later or take one day longer without moving the project end.
How Likely Is the Deadline?
PERT adds up the variances (σ²) of the critical activities: 2.78 + 0.11 + 2.78 + 0.44 + 0.44 + 0.11 = 6.67. The square root gives σ = 2.58 working days for the project. Under the normal distribution assumption of PERT:
| Committed deadline | z-value | Probability |
|---|---|---|
| 29 working days | 0.00 | 50.0% |
| 31 working days | 0.77 | 78.1% |
| 32 working days | 1.16 | 87.7% |
If you promise the client 29 days, you hit the date with the odds of a coin toss. 32 days is the more reliable commitment.
The same example shows the limit of the method. PERT only looks at the critical path. The path via ordering (B) is just one day shorter and spreads more (σ = 3.23 days). This path alone exceeds 29 days with a probability of 37.8%. The 50% for 29 days is therefore too optimistic. A Monte Carlo simulation in project management calculates all paths at once and closes this gap.
How Do You Create a PERT Chart Step by Step?
You create a PERT chart in seven steps: list the activities, define dependencies, estimate three durations, draw the network, run the forward and backward pass, mark the critical path and keep it up to date.
- Identify all activities: Derive the activities from the work breakdown structure. A mind map helps in early phases.
- Define dependencies: For every activity, decide which activities must be finished first. Activities without mutual dependency run in parallel.
- Estimate durations: Record o, m and p and calculate te. If you have reliable historical values, a single estimate is enough.
- Draw the chart: Activities as nodes, dependencies as arrows. Dependent activities sit to the right of their predecessors.
- Run the forward and backward pass: The forward pass gives earliest start and finish, the backward pass latest start and finish.
- Determine the critical path and slack: Slack = latest start minus earliest start. Activities with zero slack form the critical path.
- Review and update: Enter actual durations and recalculate the critical path after every major change.
How Do You Create a PERT Chart in Merlin Project?
In Merlin Project you build a PERT chart from the Work Breakdown: create activities, enter durations, set dependencies, then open the project view PERT in the Net Plan view type. The cards show earliest and latest start and end, expected duration and slack.
1. Create activities and record the estimates
Open View > Work Breakdown and add the seven activities with Insert > Activity (Cmd+N). Merlin Project does not calculate the three-point estimate itself. Create one custom field each for o, m and p: Insert > Column, then For new Field, field name "Optimistic" and, in the Inspector, the Type Duration. Repeat this for "Most likely" and "Pessimistic". The estimates stay documented on the activity. Enter te in the Inspector on the Plan tab in the Duration field, for example 16 days for ordering.
2. Set dependencies
Select predecessor and successor and choose Structure > Link > End to Start (Ctrl+Cmd+L). Alternatively, enter the # number of the predecessor on the Dependencies tab in the Inspector. The lesson Adding Context and Logic shows the details.
3. Show the critical path
View > Show Critical Path highlights the chain in red in the Gantt chart. The column Expected Total Slack shows the slack of every activity, 1 day for B in the example.
4. Open the PERT view
Press Cmd+2 to switch to the Net Plan and choose the project view PERT. The view option Critical Path highlights the path here as well. The Net Plan and the PERT chart are part of Merlin Project, not Merlin Project Express.
What Are the Advantages and Disadvantages of a PERT Chart?
A PERT chart makes uncertainty and bottlenecks visible but takes effort: you need three estimates and clean dependencies for every activity. With few, well-known activities the effort rarely pays off.
| Advantages | Disadvantages |
|---|---|
| Creating it forces you to think through the whole project. Open points become visible. | Creating it takes effort: three estimates per activity. |
| The network shows all activities and their dependencies at a glance. | Readers need a short introduction to nodes, arrows and slack. |
| Critical path and slack are visible immediately. | The more detailed the network, the higher the maintenance effort. |
| The spread σ puts a number on schedule risk. | PERT only looks at the critical path and underestimates parallel paths. |
| Software recalculates changes instantly. | For small projects the method is oversized. |
Tip: Network techniques such as PERT pay off in larger projects with many dependencies. For shorter projects a Gantt chart or a Kanban board is often enough.
When Should You Use PERT Instead of Gantt or Kanban?
PERT suits the planning of uncertain projects with many dependencies, Gantt the schedule control on a timeline, Kanban the ongoing flow of work. In practice many teams combine the views.
PERT vs. Gantt
- Gantt chart: Shows activities as bars on a timeline. Suited to scheduling, resources and progress.
- PERT chart: Shows the logic of the dependencies and the uncertainty of the durations. Suited to finding a reliable date before the project starts.
PERT vs. Kanban
- Kanban: Controls the flow of work and limits work in progress, typical in agile and lean contexts.
- PERT chart: Plans a fixed sequence with a critical path, typical for many interlocking activities.
PERT vs. Scrum
- Scrum: Iterative sprints for projects with changing requirements.
- PERT chart: For traditional or hybrid projects where deadlines and dependencies matter.
Note: In Merlin Project the same activity appears as a bar in the Gantt chart, as a card in the PERT network and as a card on the Kanban board. You maintain the data once.
Practical Tips
- Ask for the estimates separately: Let the people who do the work estimate o, m and p, and ask for the pessimistic value explicitly.
- Coarse first, then detailed: Start at work package level and refine only activities on or near the critical path.
- Watch near-critical paths: In the example, B has only one day of slack. Such activities belong on the same watch list as the critical path.
- Commit to dates with a probability: Give a range instead of a single date, for example 29 to 32 working days.
- Update regularly: A PERT chart is only valid as long as actual durations are entered.
Conclusion
A PERT chart combines a network diagram with three-point estimation. It delivers three results: the expected project duration, the critical path and a probability for the committed date. In the example these are 29 working days, the chain A, C, D, E, F, G and 87.7% for 32 days. For many parallel, uncertain paths a Monte Carlo simulation complements the calculation.
If you have any questions about this blog article or would like to discuss it, we look forward to your contribution in our forum.
Frequently asked questions
What is the PERT formula?
You calculate the expected duration with te = (o + 4m + p) / 6. o is the optimistic, m the most likely and p the pessimistic estimate. The standard deviation is σ = (p − o) / 6. Example: 5, 8 and 14 days give te = 8.5 days and σ = 1.5 days.
What is the difference between PERT and CPM?
Both methods use a network diagram and a critical path. The Critical Path Method (CPM) works with one fixed duration per activity. PERT works with three estimates and also delivers a spread from which you derive the probability of meeting a date.
What is the difference between a PERT chart and a Gantt chart?
The PERT chart shows the logic: which activities depend on each other, how uncertain the durations are, which path is critical. The Gantt chart shows the same activities as bars on a timeline and suits schedule control and progress tracking.
How do I calculate the probability of meeting a deadline?
Add up the variances σ² of all activities on the critical path and take the square root. Divide the difference between the committed date and the expected duration by this σ and look up the z-value in the normal distribution. In the example, 32 days with an expected 29 days and σ = 2.58 give a probability of 87.7%.
Does Merlin Project have a PERT chart?
Yes. In the Net Plan view type (Cmd+2) you choose the project view PERT. Every card shows earliest and latest start and end, expected duration and slack. You record the three estimates in custom fields of the type Duration. Net Plan and PERT are included in Merlin Project, not in Merlin Project Express.
