A PERT diagram is a project network diagram that shows activities, milestones, dependencies, and the order in which work must occur. PERT—Program Evaluation and Review Technique—also uses three duration estimates for each activity: optimistic, most likely, and pessimistic. The estimates produce a weighted expected duration that helps a team forecast completion, identify the critical path, and see where schedule flexibility exists.
What a PERT diagram shows
A PERT diagram represents a project as a network rather than a simple list of tasks. Activities are connected according to their dependencies: an activity cannot start until the work before it has reached the required point. Branches show work that can proceed in parallel, while merged branches show activities that must all be complete before the next activity begins.
Depending on the notation, a diagram may place activities in boxes or arrows and may show milestones as events. The essential information is the same: the project’s logic, estimated activity times, and the routes through the network.
NASA describes this logic as showing “which activities must be complete before others can start.” A completed network schedule can then calculate the project duration, the activities that determine it, and the spare time available to other activities.
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What the three PERT time estimates mean
- Optimistic time (O): the shortest reasonable duration when favorable conditions apply and little goes wrong.
- Most-likely time (L): the duration expected under normal working conditions, based on the team’s best judgment.
- Pessimistic time (P): the longest reasonable duration when significant but plausible problems occur. It is not an extreme impossibility.
These are planning judgments, not guarantees. Their quality depends on clearly defined activities, realistic assumptions, and useful knowledge about the work.
How PERT calculates expected duration
PERT weights the most-likely estimate more heavily than either endpoint:
M = (P + 4L + O) / 6
Here, M is the expected duration. For example, if an activity has an optimistic time of 2 days, a most-likely time of 3 days, and a pessimistic time of 5 days:
M = (5 + 4 × 3 + 2) / 6 = 19 / 6 = 3.17 days
The result is an estimate for scheduling. It should not be presented as a promised finish time or as a universal accuracy measure.
How to make a PERT chart
- List the work. Break the project into activities that have a clear start, finish, deliverable, and owner. Add important milestones separately if they mark a decision or handoff rather than work.
- Record predecessors. For each activity, write down which activities must finish before it can begin. Do not connect tasks merely because they are performed by the same person or team.
- Estimate O, L, and P. Use the same unit—such as hours, days, or weeks—for all three estimates and document major assumptions.
- Calculate expected times. Apply (P + 4L + O) / 6 to every activity. Keep the three original estimates as well as the calculated value so uncertainty remains visible.
- Draw the dependency network. Place activities in dependency order, show parallel branches where appropriate, and make every predecessor relationship explicit.
- Run a forward pass. Starting at the project beginning, calculate each activity’s earliest start and earliest finish. A task with several predecessors cannot start until its latest predecessor finishes.
- Run a backward pass. Starting from the required project finish, calculate latest allowable starts and finishes without moving that completion date.
- Calculate float and mark the critical path. Compare early and late dates. Activities with no scheduling flexibility form the time-controlling path; activities with positive float can move within that allowance.
Worked PERT example
Suppose a small project has these dependencies and illustrative estimates:
| Activity | Predecessor | O | L | P | Expected time (M) |
|---|---|---|---|---|---|
| A: research | None | 2 days | 3 days | 5 days | 3.17 days |
| B: design | A | 1 day | 2 days | 3 days | 2 days |
| C: build | A | 4 days | 6 days | 10 days | 6.33 days |
| D: test | B and C | 2 days | 3 days | 8 days | 3.67 days |
After A, activities B and C can run in parallel. D must wait for both. The two complete paths are:
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- A–B–D: 3.17 + 2 + 3.67 = 8.84 days
- A–C–D: 3.17 + 6.33 + 3.67 = 13.17 days
The longer path, A–C–D, controls the planned finish in this example. B has time available relative to C, although its exact float depends on the required finish date and the rest of the network.
What is the critical path in PERT?
The critical path is the longest time-controlling path through the network, calculated using the activity durations in the schedule. It determines the earliest possible project completion under those assumptions. A delay to an activity on that path generally delays the project unless the team changes the logic, duration, or resources.
Critical-path status is not a permanent label. Re-estimating an activity, completing work, changing dependencies, or using available float can make a different path become critical. Track the path throughout execution rather than only when the initial chart is created.
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What float or slack means
Float (also called slack) is the amount of time an activity can slip without changing a specified schedule date. Total float is measured against the project finish or another network constraint; free float describes delay that does not affect the early start of a successor.
Noncritical work can still be operationally important. Consuming its float increases the risk that the activity or an adjacent path will become critical, so float is a buffer to manage—not permission to ignore the task.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.PERT versus CPM: what is the difference?
PERT and the Critical Path Method (CPM) use the same basic network logic: define activities, connect dependencies, calculate dates, and identify the path that controls completion. Their traditional distinction is how they represent duration and uncertainty.
Best Value
| Comparison | PERT | CPM |
|---|---|---|
| Duration inputs | Three estimates: optimistic, most likely, and pessimistic | Traditionally one duration estimate per activity |
| Main emphasis | Planning under uncertain activity durations | Deterministic sequencing and schedule control |
| Risk communication | Makes uncertainty visible through the three-point estimates | Shows timing and float based on the selected single durations |
| Critical-path analysis | Uses expected times to identify the time-controlling path | Uses assigned activity times to identify the time-controlling path |
Modern scheduling practice often combines the approaches: a team may use three-point estimates to improve uncertain forecasts and CPM calculations to manage the resulting schedule.
When PERT is useful—and where it can mislead
Useful situations
- New or research-heavy projects where activity durations are uncertain.
- Projects with substantial parallel work and complicated handoffs.
- Planning discussions where the team needs to expose schedule assumptions and risk.
- Projects that need explicit visibility into float and the work controlling completion.
Common failure modes
- Vague activities: “finish product” is too broad to estimate or connect reliably. Split it into observable deliverables.
- Missing dependencies: An omitted predecessor can make the calculated finish unrealistically early.
- False precision: Reporting 3.17 days does not mean the estimate is accurate to two decimal places.
- Unrealistic pessimistic values: If P ignores credible risks, the range understates uncertainty; if it describes an impossible catastrophe, it distorts the plan.
- Static maintenance: A chart that is never updated stops reflecting the project’s actual logic and remaining work.
PERT does not guarantee a completion date, and authoritative sources do not establish a universal accuracy percentage or claim that it is best for every project. Its value is disciplined estimation and dependency analysis.
Choosing a format or tool
You can create a small PERT diagram on paper or in a spreadsheet. For larger networks, project-scheduling and network-diagram software can automate forward and backward passes, recalculate float when dates change, and highlight the current critical path. Whatever tool you use, verify the dependency logic and estimates manually; software cannot correct an incomplete activity list or an incorrect predecessor.
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