PERT estimate calculator
A PERT estimate weights three guesses for each task: expected time = (optimistic + 4 × most likely + pessimistic) ÷ 6, with a standard deviation of (pessimistic − optimistic) ÷ 6. Enter your tasks below to get each task's expected time and the project total at 50%, 80% and 90% confidence.
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E = 3.33 days, σ = 0.67
E = 6.67 days, σ = 1.33
E = 2.17 days, σ = 0.5
Expected total (P50)
12.17 days
σ = 1.57 across 3 of 3 tasks
P80
13.49 days
P90
14.18 days
A row with an error is left out of the totals. Confidence levels assume independent tasks.
#The method
How the PERT estimate is calculated
PERT (Program Evaluation and Review Technique) treats each task's duration as uncertain. The most likely value gets four times the weight of the two extremes, and the spread between optimistic and pessimistic sets the uncertainty.
To total a project, add the expected times, but add the variances rather than the standard deviations. Tasks rarely all run late together, so the project's spread grows more slowly than the sum of the tasks' spreads. Adding the standard deviations directly is a common mistake and makes the P80 and P90 too pessimistic.
The confidence levels use a normal approximation of the total: the expected time plus z standard deviations, where z is 0 for P50, 0.8416 for P80 and 1.2816 for P90. It is an approximation. It assumes the tasks are independent, so if one root cause would delay many of them, commit nearer the P90 or beyond.
- Expected time, per task
E = (O + 4M + P) ÷ 6O optimistic, M most likely, P pessimistic. Needs O ≤ M ≤ P.
- Standard deviation, per task
σ = (P − O) ÷ 6Variance is σ².
- Project total
E_total = Σ E, σ_total = √(Σ σ²)Variances add; standard deviations do not.
- Confidence level
P_k = E_total + z_k × σ_total (z: P50 0, P80 0.8416, P90 1.2816)Normal approximation of the total.
#Questions
Frequently asked questions
- What is the PERT formula?
- The PERT expected time is (optimistic + 4 × most likely + pessimistic) ÷ 6, and its standard deviation is (pessimistic − optimistic) ÷ 6. For several tasks, add the expected times and take the square root of the sum of the variances for the total standard deviation.
- What is the difference between PERT and a simple three-point average?
- A simple triangular average is (O + M + P) ÷ 3 and weights all three guesses equally. PERT weights the most likely value four times, so one extreme guess moves the estimate less.
- What do P50, P80 and P90 mean?
- They are the totals you would expect to come in at or under with 50%, 80% and 90% probability. P50 is the expected time itself: you miss it about half the time. P80 and P90 add a buffer of 0.8416 and 1.2816 standard deviations.
- Why not just add up each task's standard deviation?
- Because that assumes every task runs late at the same time. For independent tasks the variances add, so the total standard deviation is the square root of the sum of squares, which is smaller than the plain sum.
- Which unit should I use: hours, days or points?
- Any unit, as long as every task uses the same one. The results come out in the unit you entered.
#How Kavanah does it
How Kavanah turns one estimate into a range
Kavanah takes a different route to the same question. A task carries one estimate, and the confidence range comes from history instead of three guesses: the sprint planner keeps the 50th and 90th percentiles of each person's actual-to-estimate ratio across tasks completed in the last 90 days, and multiplies the estimate by them.
The range is applied only to the forecast and is never written back over the estimate, so the next calibration still measures the original number. Without enough history the planner falls back to team numbers, or tells you it is uncalibrated.
Keep reading
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