tE = (O + 4M + P) / 6
The PERT formula for the PMP exam, with a free calculator. Enter optimistic, most likely, and pessimistic values to get expected duration, standard deviation, variance, and confidence ranges, then read how the exam tests it below.
Updated September 2026
tE = (O + 4M + P) / 6
PERT stands for Program Evaluation and Review Technique. The formula takes three estimates for an activity, optimistic (O), most likely (M), and pessimistic (P), and returns an expected duration. Most likely counts four times, so the answer leans toward the outcome you'd really expect instead of splitting the difference between best and worst case. This weighted version is what PMP prep, and every exam-style question that says "PERT", means by the PERT formula.
PMBOK 8 doesn't use the phrase "three-point estimating". Its term is multipoint estimating: estimating cost or duration with an average or weighted average of optimistic, pessimistic, and most likely values when the single-point estimates are uncertain. The guide prints one formula under that entry, the triangular distribution, and describes it as one commonly used option. It names PERT separately, as one of the techniques for estimating effort and duration when you develop the schedule, without printing the weighted formula. So on the exam, "three-point", "multipoint", and "PERT" all point at the same three inputs. The distribution named in the question is what decides the math.
Beta (PERT): tE = (O + 4M + P) / 6
Triangular: tE = (O + M + P) / 3
Triangular weights all three values equally. PMBOK 8 says it fits when there's little historical data or the estimates are judgment calls. Beta weights most likely four times and is the one people mean by PERT. If a question names the distribution, use that one. If it says PERT, use beta. If it just says three-point or multipoint with no distribution, look at the answer choices: the beta and triangular results are usually both there, and the question is testing whether you know they differ.
An activity is estimated at 8 days optimistic, 11 days most likely, and 26 days pessimistic.
Two days apart from the same three numbers, because beta pulls toward the most likely value. Type 8, 11, 26 into the calculator above and you'll see the beta result, the standard deviation, and the confidence ranges.
σ = (P − O) / 6
Standard deviation measures how much uncertainty sits inside the estimate. A wide gap between pessimistic and optimistic means a risky activity. Only P and O appear in it; if an answer choice has M in a standard-deviation formula, it's wrong by construction. PMBOK 8 doesn't print this formula, it's the standard PMP-prep companion to the PERT estimate, and exam-style questions use it three ways:
PMI doesn't publish a formula list, so no one can promise you a PERT question. What's documented: the 2026 Exam Content Outline puts estimating in the Process domain, 41 percent of the exam, under "estimate work effort and resource requirements" and "estimate project tasks." PMBOK 8 lists multipoint estimating as a tool for both duration and cost estimates. Expect the formula to show up inside a scenario rather than as a bare calculation: three numbers in a paragraph, and a question about the expected duration, the range, or which activity carries the most risk.
The PERT formula for expected duration is (O + 4M + P) / 6. O is the optimistic estimate, M is the most likely estimate, and P is the pessimistic estimate. It's a weighted average that counts the most likely value four times, which pulls the result toward the outcome you'd actually expect. PMP prep and exam-style questions mean this beta-distribution version when they say PERT.
A three-point estimate uses optimistic, most likely, and pessimistic values. PMBOK 8 calls this multipoint estimating and gives the triangular version, (O + M + P) / 3, which weights all three equally. PERT is the beta version, (O + 4M + P) / 6, which weights most likely four times. Same three inputs, different answers, so read which one the question names.
PERT standard deviation is (P - O) / 6, using only the pessimistic and optimistic values. Variance is the standard deviation squared. Standard deviation sets the confidence ranges around the expected duration, about 68 percent within one standard deviation, 95 percent within two, and 99.7 percent within three. To combine activities on a path, add the variances, then take the square root.
PMI does not publish a formula list, so nobody can promise a PERT question. What's documented: PMBOK 8 names PERT as a technique for estimating effort and duration, and the 2026 exam's Process domain, 41 percent of the questions, includes estimating work effort and estimating project tasks. Know both the beta and triangular versions and the standard deviation formula, and you're covered either way.
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