PERT Chart: Formula, Examples & How to Use It [2026]

In 1958, the US Navy needed to coordinate roughly three thousand contractors on the Polaris missile program without a computer on every desk, so it invented a way to map an entire schedule as a network and reason about the parts that could not slip. That method was PERT, and it is still one of the clearest ways to plan a project full of uncertainty. Seventy years on, it is also a dependable source of exam questions. This guide covers the PERT chart in full — what it is, the three-point estimate formula, how to build one, how it compares to a Gantt chart, and how it shows up on the PMP and CAPM exams.

What is a PERT chart?

A PERT chart — short for Program Evaluation and Review Technique — is a network diagram that lays out a project's activities as a sequence of connected nodes, showing which tasks depend on which and how long the whole thing should take. Its defining feature is that it estimates durations under uncertainty, using three estimates per activity rather than a single number, which makes it especially useful early in planning when you cannot yet pin a task to one figure.

PERT was developed by the US Navy for the Polaris submarine program in the late 1950s, and it has been a core scheduling tool ever since. In practice it does three things well: it maps dependencies so you can see the order work must follow, it produces a realistic time estimate from optimistic and pessimistic bounds, and it exposes the critical path — the longest chain of dependent activities, which sets the project's minimum duration.

The PERT three-point estimate formula

The heart of PERT is the three-point estimate, which combines three durations for each activity into one expected time. You gather an optimistic (O), most likely (M), and pessimistic (P) estimate, then apply the beta (PERT) distribution, which weights the most likely value four times:

> Expected time (tE) = (O + 4M + P) / 6

For example, if an activity is estimated at 6 days optimistically, 10 days most likely, and 26 days pessimistically, its PERT expected duration is (6 + 4 × 10 + 26) / 6 = 72 / 6 = 12 days. Note that this is not the same as the simple (triangular) average of (6 + 10 + 26) / 3 = 14 days — the beta formula's four-times weighting on the most likely value pulls the estimate closer to it while still accounting for the long pessimistic tail.

PERT also measures uncertainty with the standard deviation, the spread between the optimistic and pessimistic bounds:

> Standard deviation (σ) = (P − O) / 6

For the activity above, σ = (26 − 6) / 6 ≈ 3.3 days, which tells you how much confidence to place in the estimate — a wide spread means more risk. Our PMP formulas cheat sheet collects these alongside the other schedule and earned-value formulas worth memorizing.

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How to make a PERT chart

Building a PERT chart is a five-step process that turns a task list into a network you can reason about:

1. List the activities. Break the project into its individual tasks, the same way you would when building a work breakdown structure.
2. Determine the dependencies. For each activity, decide which tasks must finish before it can start. These relationships define the shape of the network.
3. Draw the network. Represent each activity as a node and connect them with arrows in dependency order, so the diagram flows from the project's start to its finish.
4. Estimate each activity. Apply the three-point estimate to every task to get its expected duration, using optimistic, most likely, and pessimistic figures.
5. Find the critical path. Add the durations along each path through the network; the longest is the critical path, and it determines the shortest time in which the project can finish.

PERT chart symbols: how to read one

A PERT chart is drawn with only two kinds of symbols, but there are two drawing conventions, and knowing which one you are looking at prevents most misreadings. In the modern activity-on-node (AON) style — the one nearly all software draws — each box (node) is an activity, labeled with its name and expected duration, and each arrow is a dependency showing what must finish before what starts. In the original activity-on-arrow (AOA) style, the logic flips: the arrows are the activities and the numbered circles are events, the moments when activities start or finish. AOA sometimes needs a dummy activity, a dashed zero-duration arrow that exists only to show a dependency the layout cannot otherwise express.

Reading either style is the same three questions: What must happen before this activity? (follow the arrows backward.) What does this activity unlock? (follow them forward.) And which chain of arrows is longest? (that is the critical path, often drawn bold or in red.) Any activity not on that longest chain has float, and the gaps you can see in the network are where that float lives.

A worked PERT chart example

Here is the whole method on one small project — a five-activity server-room upgrade. Each activity gets three-point estimates, and the beta formula turns them into expected durations:

The network has two paths from start to finish: A→B→D totals 4 + 6 + 9 = 19 days, and A→C→E totals 4 + 7 + 2 = 13 days. The longer one is the critical path, so the project's expected duration is 19 days — and the 13-day path has 6 days of float.

Now the part tool-vendor guides skip: how much confidence does 19 days deserve? Add the critical path's variances (σ² of A, B, and D) and take the square root: √(0.67² + 1.67² + 2.00²) ≈ 2.7 days. Expected duration 19 means finishing by day 19 is roughly a coin flip; committing at about one standard deviation above — day 22 — raises the confidence to roughly 84%. The σ column also shows where the risk lives: B and D carry the widest spreads, so those two estimates deserve the hardest scrutiny. When several paths run close together this single-path arithmetic understates the risk, which is where Monte Carlo simulation takes over.

When to use a PERT chart

A PERT chart earns its keep in the planning phase of uncertain work — projects with little history behind their estimates, exactly the situation it was invented for on Polaris. Reach for it when the dependencies matter more than the dates, when estimates are honest ranges rather than known figures, or when a sponsor needs a duration with a stated confidence level instead of a hopeful single number. Once execution starts, the Gantt chart's calendar view takes over for day-to-day tracking; the PERT chart's job is done when the plan it produced is trusted.

PERT chart vs. Gantt chart

PERT charts and Gantt charts are often compared because both plan schedules, but they do different jobs. A PERT chart is a flowchart that emphasizes dependencies and sequence, which makes it strongest during planning, when you are working out how tasks relate and where the critical path runs. A Gantt chart is a timeline of bars against a calendar, which makes it strongest during execution, when you are tracking progress and dates.

In practice the two are complements rather than rivals: many teams use a PERT chart to plan the network and estimate durations, then build a Gantt chart to run and monitor the work. Both rely on the same underlying critical path.

PERT vs. CPM

PERT and the critical path method (CPM) were born in the same era — PERT on the Navy's Polaris program, CPM at DuPont — and both work on the same activity network. The difference is what they assume about durations. CPM is deterministic: each activity gets one fixed estimate, which suits maintenance and construction work with solid history, and it extends naturally into cost trade-offs such as crashing and fast-tracking. PERT is probabilistic: three-point estimates and standard deviations, built for first-of-a-kind work where durations are ranges. Modern scheduling quietly merges them (a network and critical path from CPM, with PERT's beta-weighted durations feeding it), which is why the exam treats the two as complementary rather than rivals.

Advantages and limitations of PERT

PERT's strengths are why it has lasted. It produces more realistic estimates than a single guess by building in optimistic and pessimistic bounds, it makes dependencies and the critical path visible, and it is a strong communication tool for showing stakeholders how a schedule fits together.

Its limitations are the flip side of that. The three-point estimates are still subjective — a PERT chart is only as good as the estimates fed into it — and the network can become complex and hard to read on very large projects. It also focuses on time and dependencies rather than resources or cost, so it is one tool in a scheduling toolkit rather than the whole kit. Used for what it is good at, though, it remains one of the clearest ways to plan under uncertainty.

PERT and three-point estimating on the PMP® and CAPM® Exams

In the PMP exam, PERT shows up less as "draw a chart" and more as a calculation and a judgment call. Expect at least one question that gives you optimistic, most likely, and pessimistic figures and asks for the expected duration — the trap is reaching for the simple average when the scenario calls for the beta formula, (O + 4M + P) / 6, or the reverse. Know both the beta and the triangular, (O + M + P) / 3, and read the question for which distribution it specifies. You may also be asked for the standard deviation, (P − O) / 6, or to reason about which activity carries the most schedule risk based on a wide spread.

Just as important is recognizing when three-point estimating is the right answer. When a scenario describes high uncertainty, a new type of work, or estimates that vary widely between experts, three-point estimating is usually the technique PMI expects, over a single-point estimate. The CAPM tests the same idea at a gentler level: the questions are shorter and lean toward recognizing the formula and computing a clean result rather than layering in risk judgment, but the underlying knowledge is identical. For a structured way to lock in these formulas and the reasoning behind them, our PMP Complete Study Guide works through every schedule technique from scratch.

PMP Practice Question: Three-Point Estimating

The riskiest activity on a project's critical path has an optimistic estimate of 8 days, a most likely estimate of 11 days, and a pessimistic estimate of 26 days. The sponsor, tired of missed dates, asks the project manager for a duration they can be reasonably confident in — roughly 84%, about one standard deviation above the expected duration.

Using PERT three-point estimating, what duration should the project manager quote?

a) 11 days — the most likely estimate, since it is the team's best single guess.

b) 13 days — the PERT expected duration from the beta formula.

c) 15 days — the average of the three estimates.

d) 16 days — the PERT expected duration plus one standard deviation.

Correct answer: D.

Rationale: Two formulas, applied in order. The beta (PERT) expected duration weights the most likely value four times: (8 + 4 × 11 + 26) / 6 = 78 / 6 = 13 days. The standard deviation spans the bounds: (26 − 8) / 6 = 3 days. The sponsor asked for roughly 84% confidence, which sits about one standard deviation above the expected value: 13 + 3 = 16 days. Choice b) is the correct expected duration but the wrong answer to the question asked, because an expected value is roughly a coin flip, not "reasonably confident." Choice c) is the subtle formula trap: (8 + 11 + 26) / 3 = 15 is the triangular average, which ignores the beta weighting and lands close enough to 16 to tempt anyone unsure which formula PERT uses. Choice a) is the single guess the whole technique exists to replace, and with a pessimistic tail stretching to 26 days it is the least defensible number on the page. To drill formula questions where the wrong answers are real mistakes, work through our PMP practice exams or, at the entry level, our CAPM practice exams.

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