How to use the three point estimate calculator
- Enter a unit of time such as days or hours, used as a label.
- For each task, enter a best case, a most likely and a worst case estimate in that unit. The values must rise from the first to the last.
- Use Add a task to estimate a whole project.
- Read the expected time, the standard deviation and the one standard deviation range.
Formula
Expected value of a task = (best case + 4 x most likely + worst case) / 6
Standard deviation of a task = (worst case - best case) / 6
Expected total = the sum of the task expected values
Standard deviation of the total = square root of the sum of the squared task standard deviations
The weights 1, 4 and 1 are the PERT weighting. The simple average of the three points, (best case + most likely + worst case) / 3, is shown for comparison.
Estimates of 2, 4 and 12 days
For a task with a best case estimate of 2 days, a most likely estimate of 4 and a worst case estimate of 12, the expected time is (2 + 4 x 4 + 12) / 6 = 30 / 6 = 5 days. The standard deviation is (12 - 2) / 6 = 1.67 days, so one standard deviation either side is 3.33 to 6.67 days. The simple average of the three is 6 days.
For three tasks of (2, 4, 12), (3, 5, 9) and (1, 2, 3) hours, the expected times are 5, 5.33 and 2, for a total of 12.33 hours. The task standard deviations are 1.67, 1 and 0.33, and the total standard deviation is the square root of 2.78 + 1 + 0.11, which is 1.97.
Why use three numbers
One number hides how unsure you are. Asking for a best case, a usual case and a worst realistic case makes you think about what could go wrong, and the gap between the best case and worst case values becomes a measure of the uncertainty. Weighting the most likely value four times keeps the usual case from being swamped by the extremes.
Because worst case estimates are often further from the most likely value than best case ones, the PERT mean usually lands above the most likely value, as in the example, where 5 days is above 4.
Limits of the method
The formula only turns your three guesses into one figure, so it is no better than those guesses. Adding variances assumes the tasks are independent, and the one standard deviation range is not a promise that work will finish inside it. Tasks that run at the same time are not handled, because the total here is a sum of the task times.
For a larger plan, use the project planner template. To turn person hours into days for a crew, try the crew hours and duration calculator, and to understand spread, see the standard deviation calculator and the average calculator.
Assumptions and limits
- Every task uses the same unit of time, and values go from best case up to most likely up to worst case.
- The expected value uses the 1-4-1 PERT weights and the standard deviation uses one sixth of the range.
- Task times are independent, so variances add.
- Tasks are done one after another, so the total is the sum of task times.
Frequently asked questions
What is the three point estimate formula?
The PERT formula is (best case + 4 x most likely + worst case) / 6. With 2, 4 and 12 it gives 5.
How is the standard deviation calculated?
In the standard PERT approach it is one sixth of the difference between the worst case and best case estimates. For 2 and 12 that is 1.67.
What is the difference between the PERT mean and the simple average?
PERT weights the most likely value four times, so it leans toward the usual case. The simple average counts each of the three points equally.
How do I estimate a project with many tasks?
Add a row for each task. The expected times add together, and the standard deviation of the total combines the task spreads as the square root of the summed squares.