PERT – the Program Evaluation and Review Technique – was developed in 1958 for the US Navy’s Polaris missile programme to plan thousands of tasks whose durations nobody could predict exactly. Instead of a single guess, each task gets three: an optimistic time O (if everything goes well), a most likely time M and a pessimistic time P (if things go wrong, short of disaster).
The estimates are blended with weights 1-4-1, based on the beta distribution, so the most likely value dominates while the extremes pull the expected time towards the risky side. The spread between pessimistic and optimistic divided by six gives a standard deviation. Assuming the total is roughly normal, you can then turn a deadline into a probability, or a probability into a deadline you can safely promise.
Project managers use it for single tasks and for whole critical paths (add the expected times and add the variances). It works for anything uncertain – software features, building work, writing a thesis or planning a move.
How to use the PERT Calculator
- Optimistic estimate (O)
- Most likely estimate (M)
- Pessimistic estimate (P)
- Target / desired completion time (optional, 0 = none)
- Confidence level for a commitment
- Time unit (for labels only)
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the three estimates in the same unit. The calculator computes E and σ, the simple triangular average for comparison, the z-score and probability for your target, and E + z·σ for the confidence level you want.
Worked example
Building a fence: O = 5, M = 7, P = 9 days. E = (5 + 28 + 9) ÷ 6 = 7 days and σ = 4 ÷ 6 = 0.667 days. For a deadline of 8 days, z = (8 − 7) ÷ 0.667 = 1.5, so the chance of finishing on time is Φ(1.5) = 93.3%. To be 95% sure, commit to 7 + 1.645 × 0.667 = 8.1 days.
Confidence levels
| Confidence | z | Commit to |
|---|---|---|
| 50% | 0 | E |
| 80% | 0.84 | E + 0.84σ |
| 90% | 1.28 | E + 1.28σ |
| 95% | 1.645 | E + 1.645σ |
| 99% | 2.33 | E + 2.33σ |
Inputs explained
| Field | What to enter |
|---|---|
| Optimistic estimate (O) | A number |
| Most likely estimate (M) | A number |
| Pessimistic estimate (P) | A number |
| Target / desired completion time (optional, 0 = none) | A number |
| Confidence level for a commitment | In % |
| Time unit (for labels only) | Choose one: days, hours, weeks, months |
What each result means
- PERT estimate (expected time) = ([Optimistic estimate (O)] + 4×[Most likely estimate (M)] + [Pessimistic estimate (P)])÷6
- Standard deviation = ([Pessimistic estimate (P)] – [Optimistic estimate (O)])÷6
- Variance = [Standard deviation]^2
- Triangular estimate (O + M + P) ÷ 3 = ([Optimistic estimate (O)] + [Most likely estimate (M)] + [Pessimistic estimate (P)])÷3
- 95% range – from = [PERT estimate (expected time)] – 1.96×[Standard deviation]
- 95% range – to = [PERT estimate (expected time)] + 1.96×[Standard deviation]
- Time to commit to at the chosen confidence = [PERT estimate (expected time)] + ninv([Confidence level for a commitment]÷100)×[Standard deviation]
Formula
PERT estimate E = (O + 4M + P) ÷ 6 · standard deviation σ = (P − O) ÷ 6 · z = (target − E) ÷ σ · P(finish by target) = Φ(z) · time at confidence c = E + Φ⁻¹(c) · σ
Worked example
Inputs — Optimistic estimate (O): 5; Most likely estimate (M): 7; Pessimistic estimate (P): 9; Target / desired completion time (optional, 0 = none): 8; Confidence level for a commitment: 95 %; Time unit (for labels only): days.
Results — PERT estimate (expected time) = 7; Standard deviation = 0.667; Variance = 0.4444; Triangular estimate (O + M + P) ÷ 3 = 7; 95% range – from = 5.693; 95% range – to = 8.307; Z-score of the target = 1.5; Probability of finishing by the target = 93.32 %; Time to commit to at the chosen confidence = 8.097; Check = Estimates are in order (O ≤ M ≤ P).
Key terms
- Optimistic time (O)
- The shortest realistic duration if everything goes right.
- Most likely time (M)
- The duration you expect in normal conditions.
- Pessimistic time (P)
- The longest realistic duration if things go wrong (excluding catastrophes).
- Critical path
- The longest chain of dependent tasks; it sets the project duration.
Frequently asked questions
What is the PERT formula?
E = (O + 4M + P) ÷ 6 and σ = (P − O) ÷ 6. With O = 5, M = 7 and P = 9 days, E = 7 days and σ = 0.67 days.
What is the difference between PERT and triangular estimates?
The triangular average (O + M + P) ÷ 3 weights all three equally; PERT gives the most likely value four times the weight, so it is less sensitive to extreme guesses.
How do I find the probability of meeting a deadline?
Compute z = (deadline − E) ÷ σ and look up the normal distribution. A deadline of 8 days gives z = 1.5 and about 93.3%.
How do I combine several tasks?
For tasks in sequence add the expected times and add the variances (σ²), then take the square root for the total standard deviation.
Why divide by 6?
Roughly 99.7% of a normal distribution lies within ±3σ, so the range from O to P is treated as six standard deviations.
Where does the 1-4-1 weighting come from?
From approximating the mean of a beta distribution, which can be skewed to model tasks that are more likely to overrun than finish early.