Project Timeline Estimator

Estimates given as a single number ('this will take 3 weeks') are almost always wrong, because projects have variance and the right answer is a range with a confidence level.

This estimator uses three-point estimation (PERT): you give it best-case, most-likely, and worst-case durations for each task, and it computes a weighted average and standard deviation. Tasks chain into a critical path, and the overall project gets an expected duration plus 80% and 95% confidence intervals.

The key insight built in: if you only have a most-likely number, you'll consistently underestimate, because there's much more upside variance (things going wrong) than downside (things going better than expected). Forcing yourself to put a worst-case on each task surfaces hidden risk and produces estimates that are more honest about uncertainty.

PERT's three-point math: expected duration = (optimistic + 4 × likely + pessimistic) / 6. The variance for each task is ((pessimistic − optimistic) / 6)². For a sequence of tasks on the critical path, the total variance is the sum of individual variances (assuming independence), so the standard deviation of the total is the square root of the summed variances. This lets you express the project duration as 'expected = X days, 80% confidence interval = X ± 1.28σ days' — a calibrated forecast rather than a single guess.

The pain this addresses: 'when will it ship?' answered as a single date that everyone treats as a commitment. Software projects in particular blow through single-point estimates routinely because there's no asymmetric upside — you can't ship faster than your most optimistic case, but you can ship arbitrarily later than your worst. PERT forces honesty about that asymmetry by requiring you to write down the worst case, which is the number that produces the most realistic forecast.

Worked example: three sequential tasks. Task A: optimistic 2 days, likely 3, pessimistic 5. Expected: (2 + 12 + 5)/6 = 3.17. Task B: 1, 2, 4. Expected: (1 + 8 + 4)/6 = 2.17. Task C: 3, 5, 10. Expected: (3 + 20 + 10)/6 = 5.5. Total expected: 10.83 days. Sum of variances: (3/6)² + (3/6)² + (7/6)² = 0.25 + 0.25 + 1.36 = 1.86. σ = 1.36 days. 80% confidence interval: 10.83 ± 1.28 × 1.36 = 9.1 to 12.6 days. Notice the asymmetric tasks (Task C with a large pessimistic case) drive most of the variance. The single-point sum (3 + 2 + 5 = 10) underestimates by nearly a day.

Where PERT's assumptions break: dependencies between tasks. The variance addition assumes task durations are independent. In real projects, they often aren't — a project where one task hits its worst case often has correlated problems on others (sick team, infra outage, scope creep affecting everything). The model under-predicts the worst-case overall when this happens. Practical workaround: stress-test by manually adding a 'risk buffer' on top of the calculated 95% interval, especially for high-stakes deadlines where you can't afford to be late.