PERT Calculator
PERT adds expected times along the critical path, tₑ = (a + 4m + b)/6: these three activities give Te = 15.3333 with an 88.7 % chance of finishing by 17.
Optimistic a, most likely m and pessimistic b times for each activity on the critical path.
15.3333333333333
Full answer, then cut to fewer decimals (not rounded):
- 15.3333333333333
- 15.333333333333
- 15.33333333333
- 15.3333333333
- 15.333333333
- 15.33333333
- 15.3333333
- 15.333333
- 15.33333
- 15.3333
- 15.333
- 15.33
- 15.3
- Project variance σ²
- 1.88889
- Project standard deviation σ
- 1.37437
- z = (T − Te)/σ
- 1.21268
- Probability of finishing by 17
- 88.737 %
| Activity | a | m | b | tₑ = (a + 4m + b)/6 | σ² = ((b − a)/6)² |
|---|---|---|---|---|---|
| 1 | 2 | 4 | 6 | 4 | 0.444444 |
| 2 | 3 | 5 | 9 | 5.33333 | 1 |
| 3 | 4 | 6 | 8 | 6 | 0.444444 |
Step-by-step solution
- tₑ = (a + 4m + b)/6 for each activity; Te = Σtₑ = 15.3333
- σ = √Σσ² = √1.88889 = 1.37437
- z = (17 − 15.3333) ÷ 1.37437 = 1.21268 → P = 88.737 %
PERT Formula
tₑ = (a + 4m + b)/6, σ² = ((b − a)/6)²
z = (T − Σtₑ)/√Σσ² on the critical path
Worked Example
Critical-path activities (2, 4, 6), (3, 5, 9) and (4, 6, 8) with a target of 17:
- tₑ = (a + 4m + b)/6 for each activity; Te = Σtₑ = 15.3333
- σ = √Σσ² = √1.88889 = 1.37437
- z = (17 − 15.3333) ÷ 1.37437 = 1.21268 → P = 88.737 %
Project standard deviation σ: 1.37437 · z = (T − Te)/σ: 1.21268 · Probability of finishing by 17: 88.737 %
| Activity | a | m | b | tₑ = (a + 4m + b)/6 | σ² = ((b − a)/6)² |
|---|---|---|---|---|---|
| 1 | 2 | 4 | 6 | 4 | 0.444444 |
| 2 | 3 | 5 | 9 | 5.33333 | 1 |
| 3 | 4 | 6 | 8 | 6 | 0.444444 |
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Frequently asked questions
Why is PERT variance added only along the critical path?
Project duration is the length of the critical path; assuming independent activities, its variance is the sum of their variances.
What is the difference between PERT and CPM?
CPM uses one deterministic time per activity; PERT uses three estimates and a beta distribution to give a probability of completion.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). PERT Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/pert-calculator/
IEEE
Scientific Converters, "PERT Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/pert-calculator/