Three-Point Project Duration Estimator

Method and input definitions

Let O, M, and P be optimistic, most-likely, and pessimistic hours, with span d = P − O. For d > 0 and user-entered concentration λ, beta-PERT uses α = 1 + λ(M − O)/d and β = 1 + λ(P − M)/d. Its mean is (O + λM + P)/(λ + 2), and its variance is d²αβ/[(λ + 2)²(λ + 3)]. λ = 4 is the common default; changing λ changes the distribution shape as well as the estimated spread.

Worked example

For O = 4, M = 8, P = 16 hours and λ = 4, the PERT mean is (4 + 4 × 8 + 16)/6 = 8.67 hours. α = 2.33 and β = 3.67 give a beta-PERT standard deviation of 2.21 hours; the entered range is 4–16 hours.

Assumptions and limits

This assumes a scaled beta-PERT distribution over the entered endpoints and mode. The standard deviation describes that modeled distribution; it is not a confidence interval or completion guarantee. Three-point estimates and λ are subjective inputs. When O = M = P, the estimate is that value with zero spread. Estimates must use one consistent unit.

Inputs are bounded to finite values shown in the form. Displayed results are rounded for readability (probability percentages and proportion fractions to four, other measures to two decimal places); whole-count outputs remain exact. A changed field clears a prior result so an outdated estimate is not presented as current.

References and related tools

These are direct calculations over user-supplied values; no external empirical benchmark is assumed.

• Task Time Estimator
• Deadline Countdown

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