PERT Calculator: Three-Point Estimation Formula and Worked Example
Three-point estimation (PERT) forces estimators to express the uncertainty in their estimate, not just the best-case number. Enter your optimistic, most likely, and pessimistic figures below to get the PERT expected value, standard deviation, and a confidence-weighted budget. It is the simplest probabilistic estimating technique and the foundation of PERT scheduling.
PERT Calculator
Enter your three estimates (cost or duration). Returns the PERT expected value, standard deviation, and confidence-weighted budget.
The PERT formula
where O is the optimistic estimate (best case), M is the most likely estimate, and P is the pessimistic estimate (worst case). The PERT formula assumes a beta distribution, which puts more weight on the most-likely value than a simple arithmetic mean would.
A simpler triangular-distribution variant uses E = (O + M + P) / 3, which gives a slightly higher expected value because it weights the tail more.
Worked example
You are estimating the cost of building a custom data migration module. The team gives:
- Optimistic (O): 30,000 USD (everything fits, no edge cases)
- Most likely (M): 50,000 USD
- Pessimistic (P): 120,000 USD (legacy schema is a mess, two months of cleanup)
So the PERT expected cost is ~58,333 USD with one standard deviation of ~15,000 USD. A budget set at E + 1 SD = 73,333 USD gives roughly 84% probability of staying within budget; E + 2 SD = 88,333 USD gives roughly 98% probability.
Crucially, the most-likely estimate alone was 50,000 USD. PERT recommends 58,333 USD just to break even, and a confidence-weighted budget closer to 73,000 USD. A single-point budget at the most-likely value would have under-funded the work.
Sources
- Project Management Institute (2017). A Guide to the Project Management Body of Knowledge (PMBOK Guide), 6th edition. PMI, Newtown Square PA. See section 6.4.2.4 on estimation.
- Malcolm D.G., Roseboom J.H., Clark C.E., Fazar W. (1959). Application of a technique for research and development program evaluation. Operations Research 7(5).
Frequently asked questions
What is the PERT formula?
The PERT formula for the expected value is E = (O + 4M + P) / 6, where O is the optimistic estimate, M is the most likely estimate, and P is the pessimistic estimate. The standard deviation is SD = (P - O) / 6. PERT assumes a beta distribution, which weights the most likely value four times more heavily than the two extremes.
How do you calculate a three-point estimate?
Collect three estimates for the cost or duration: optimistic (O), most likely (M), and pessimistic (P). Apply the PERT weighted formula E = (O + 4M + P) / 6 for a beta distribution, or the simpler triangular average E = (O + M + P) / 3. With O = 30,000, M = 50,000 and P = 120,000, the PERT expected value is (30,000 + 200,000 + 120,000) / 6 = 58,333.
What is the difference between the PERT (beta) and triangular formula?
The PERT (beta) formula E = (O + 4M + P) / 6 multiplies the most likely value by four, so the estimate sits close to M. The triangular formula E = (O + M + P) / 3 weights all three values equally, producing a higher expected value when the pessimistic tail is long. PERT is the PMBOK default; the triangular form is used when the most likely value is not clearly more probable than the extremes.
How do you turn a PERT estimate into a budget confidence level?
Add multiples of the standard deviation to the expected value. A budget set at E + 1 SD covers roughly 84% of outcomes; E + 2 SD covers about 98%. With E = 58,333 and SD = 15,000, an 84% budget is 73,333 and a 98% budget is 88,333. The single most-likely value of 50,000 would have under-funded the work.