About the PERT Estimate Calculator
This PERT estimate calculator converts a three-point estimate — optimistic, most likely and pessimistic — into a single expected duration using the Program Evaluation and Review Technique (PERT) beta approximation. It also gives the standard deviation, 68% and 95% ranges, the duration you can commit to at a chosen confidence level, and the probability of finishing by a target date or budget.
Project managers, developers estimating sprints, contractors quoting jobs and students studying for the PMP exam can use it for a single activity, or switch to task-list mode and paste one task per line to roll several sequential tasks into a total estimate. In list mode the expected times add up and the variances add up, so the combined uncertainty is smaller than the sum of the individual ranges.
PERT assumes the three estimates are honest and independent and approximates the total with a normal distribution, which works best when several tasks are combined. The units are whatever you use — hours, days, weeks or story points — and the same formula works for cost estimates.
With the default inputs, the pert expected estimate (e) is 16. Change any value above to recalculate instantly.
How to use the pert estimate calculator
- 1Choose a single task or a list of sequential tasks.
- 2Enter optimistic, most likely and pessimistic estimates (or one task per line).
- 3Pick the unit you are estimating in.
- 4Enter a target or deadline and the confidence level you want to commit to.
- 5Use the expected estimate for planning and the confidence estimate for promises.
Formula and method
PERT approximates each activity with a beta distribution whose mean is the weighted average of the three estimates, with the most likely value counted four times. The standard deviation is one-sixth of the range between the pessimistic and optimistic values, on the idea that the range spans about six standard deviations.
For a chain of sequential tasks the expected times add, and — assuming tasks are independent — so do the variances, so the total standard deviation is the square root of the summed variances. The probability of meeting a target uses the normal distribution (by the central limit theorem) with z = (target − E) ÷ σ, and the commitment estimate at a confidence level is E + z × σ. The simple average (O + M + P) ÷ 3 is shown for comparison; it gives more weight to the tails.
- O
- Optimistic (best-case) estimate
- M
- Most likely estimate
- P
- Pessimistic (worst-case) estimate
- E
- PERT expected value
- σ
- Standard deviation
- Φ
- Standard normal cumulative distribution function
Worked examples
Single task: 10 / 15 / 26 days
E = (10 + 4 × 15 + 26) ÷ 6 = 16 days and σ = (26 − 10) ÷ 6 ≈ 2.67 days. An 18-day deadline is 0.75σ above the mean, about a 77% chance. To be 90% confident, commit to 16 + 1.2816 × 2.67 ≈ 19.4 days.
Three sequential tasks
Design (E 5.33, σ 1), build (E 12.67, σ 2) and test (E 4.33, σ 1) total 22.33 days. Variances 1 + 4 + 1 = 6 give σ ≈ 2.45. A 25-day deadline has about an 86% chance, and a 95% commitment is 22.33 + 1.645 × 2.45 ≈ 26.4 days.
Software feature in hours
E = (4 + 24 + 14) ÷ 6 = 7 hours and σ = 10 ÷ 6 ≈ 1.67. Finishing within 8 hours (z = 0.6) has about a 72.6% chance; an 80% commitment is 7 + 0.8416 × 1.67 ≈ 8.4 hours.
Frequently asked questions
What is the PERT formula?+
The PERT expected time is E = (O + 4M + P) ÷ 6, where O is the optimistic, M the most likely and P the pessimistic estimate. The standard deviation is (P − O) ÷ 6.
What is the difference between PERT and a triangular three-point estimate?+
The triangular estimate is a simple average, (O + M + P) ÷ 3, giving each value equal weight. PERT weights the most likely value four times, so it stays closer to M and is less pulled by an extreme pessimistic value.
How do I combine PERT estimates for several tasks?+
For tasks done one after another, add the expected times and add the variances (σ²), then take the square root for the total standard deviation. Do not add standard deviations directly — that overstates the uncertainty.
What does a 95% confidence estimate mean?+
It is the duration you have about a 95% chance of beating under the PERT normal approximation, calculated as E + 1.645σ. Use it for external commitments; use E for internal planning.
Is PERT on the PMP exam?+
Three-point estimating appears in PMI’s PMBOK Guide and is a common PMP exam topic. Candidates should recognize both the beta (PERT) formula (O + 4M + P) ÷ 6 and the triangular average (O + M + P) ÷ 3, and the σ = (P − O) ÷ 6 approximation.
Can PERT be used for cost estimates?+
Yes. The same formula works for any quantity with best, likely and worst cases — costs, story points or effort hours. Just enter the three cost figures instead of durations.