Three-Point Estimate Calculator
Commit to the 85th percentile, not the expected value.
Work out Three-Point Estimate. Commit to the 85th percentile, not the expected value. Shows the working, not just the answer.
PERT expected value
11.7 days
Commit to 15.1 days for an 85% chance of making it
The PERT weighting counts the most likely case four times, which keeps the estimate anchored to reality while still letting a long tail move it. It gives 11.7 where a simple average of the three would give 13.3 — a difference that grows with the skew, and real estimates are almost always skewed long because there are far more ways for work to take longer than to finish early. The standard deviation is what turns a number into a commitment. Quoting the expected value means roughly a coin flip on making it; quoting the 85th percentile means committing to 15.1 days and usually delivering early, which is a far better position than the reverse. A spread ratio above about 4 suggests the work is not understood well enough to estimate yet.
How the Three-Point Estimate Calculator works
PERT expected value, standard deviation and confidence ranges from an optimistic, most likely and pessimistic estimate. The standard deviation is what turns a single number into a commitment you can actually make.
Also known as: pert · three point estimate · pert formula · optimistic pessimistic · project estimate · estimation confidence · 85th percentile estimate · beta distribution estimate · expected duration · estimate range
Why the most likely case counts four times
The PERT formula is (optimistic + 4 × most likely + pessimistic) ÷ 6. The heavy weighting on the realistic case keeps the estimate anchored while still letting a long tail move it.
A simple average gives the extremes equal footing with the realistic case, which is wrong in a specific direction: estimates are almost always skewed long, because there are far more ways for work to take longer than to finish early.
For 5, 10 and 25, PERT gives 11.67 and a simple average gives 13.33. The gap grows with the skew, and it is the difference between an estimate that reflects the likely outcome and one dominated by a worst case nobody expects.
The standard deviation is the useful half
The expected value is a coin flip. Committing to it means missing roughly half the time, which is not what anyone means when they give a date.
The standard deviation — the range divided by six — turns the estimate into a distribution, and the 85th percentile is the usual commitment point. Quoting that means usually delivering early, which is a far better position to negotiate from than the reverse.
It also gives a sanity check. A pessimistic case more than about four times the optimistic one means the work is not understood well enough to estimate, and investigating to narrow the range is worth more than any refinement of the arithmetic.
Combining estimates across a project
Add the expected values, and add the variances rather than the standard deviations. That is the part people get wrong, and it works in your favour.
Because variances add, total uncertainty grows more slowly than the total duration. Ten tasks each with a two-day standard deviation combine to a project standard deviation of about 6.3 days, not 20.
So a project made of many uncertain tasks is more predictable than any single one of them, provided the uncertainties are genuinely independent. Where they are not — a shared dependency, one person on everything, a single risky assumption underneath several tasks — that correlation is exactly what makes projects overrun together rather than averaging out.
Where to go next
The Three-Point Estimate question rarely arrives on its own. These are the ones that usually come with it:
- Sprint Velocity Calculator — A range is the honest form of a software estimate.
- Little's Law Calculator — Halve the work in progress and the lead time halves with it.
- Team Capacity Calculator — Contracted hours are not available hours.
- Ring Size Calculator — Finger measurement to US, UK, EU and Japanese sizes.
Frequently asked questions
What is the PERT formula?
(optimistic + 4 × most likely + pessimistic) ÷ 6. The weighting of four keeps the estimate anchored to the realistic case while still letting a long tail move it.
Why not just average the three?
Because a simple average gives the extremes as much weight as the realistic case, and estimates are almost always skewed long — there are far more ways for work to take longer than to finish early.
What confidence should I commit to?
The 85th percentile is the usual commitment point. Quoting the expected value means roughly a coin flip on making it; quoting the 85th means usually delivering early, which is a far better position.
How is the standard deviation calculated?
The range divided by six, on the assumption that the optimistic and pessimistic cases are about three standard deviations either side of the mean. It is a convention, and it is a serviceable one.
What if my range is very wide?
A pessimistic case more than about four times the optimistic one suggests the work is not understood well enough to estimate. Narrowing the range through investigation is worth more than any refinement of the arithmetic.
Does this work for a whole project?
Estimate the tasks separately and add the expected values; variances add rather than standard deviations, so the combined uncertainty grows more slowly than the total. A project of many uncertain tasks is more predictable than any single one of them.
Where does the PERT weighting come from?
The programme evaluation and review technique developed for the US Navy Polaris programme in the 1950s. The four-times weighting on the most likely case approximates a beta distribution and has survived on results.
Who should provide the three numbers?
The people doing the work, independently before discussing. Estimates anchored by whoever speaks first are systematically worse, and the spread between people is itself information.
What is the optimistic case supposed to mean?
Everything goes right — no interruptions, no surprises, no waiting. It is not the best you have ever done and it is not achievable routinely, which is why it carries so little weight in the formula.
How do I combine estimates across tasks?
Add the expected values, and add the variances rather than the standard deviations. Total uncertainty grows more slowly than the total, so a project of many uncertain tasks is more predictable than any single one.
Does this fix optimism bias?
It reduces it and does not remove it, because all three inputs come from the same optimistic person. The most reliable correction is comparing estimates against what similar past work actually took.
Should I quote the range or a single number?
The range, with the confidence level named. 'Ten to eighteen days, and I would commit to sixteen' communicates more in one sentence than any single figure can.
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