Three-point estimates that show the uncertainty

Why three points beat one guess

A single duration or cost estimate hides the conditions behind it. Three-point estimating makes those conditions explicit with an optimistic value, a most-likely value and a pessimistic value. The calculator compares a triangular average with the weighted PERT, or beta, estimate, then translates the spread into standard deviation, variance and confidence ranges.

The method works for a duration, a cost or another measurable quantity. Choose one unit and use it for all three inputs. If the points are weeks, every result is in weeks. If they are thousands of currency units, the outputs use that same scale. The points must describe the same scope, team and assumptions. A best case for a small release combined with a worst case for the full release is not uncertainty; it is a mismatched boundary.

Triangular and PERT formulas

Triangular = (O + M + P) ÷ 3
PERT = (O + 4M + P) ÷ 6
σ = (P − O) ÷ 6
Variance = σ²

The triangular result gives every point equal weight. It is transparent and useful when the three scenarios are similarly plausible. PERT gives the most-likely value four times the weight of either extreme because most work clusters around a normal case rather than landing at a lucky or disastrous boundary. The weighted result is therefore usually closer to M, while the standard deviation describes the width of the uncertainty rather than a second forecast.

Worked example: a six-week activity

Enter O = 4 weeks, M = 6 weeks and P = 12 weeks. The triangular estimate is 7.33 weeks. PERT is (4 + 4×6 + 12) ÷ 6, or 6.67 weeks. Standard deviation is (12 − 4) ÷ 6, or 1.33 weeks, and variance is about 1.78 weeks squared.

A one-standard-deviation working range around PERT is 5.33 to 8.00 weeks. The calculator shows 68% confidence as that approximate band, 95% as PERT plus or minus two standard deviations, and 99.7% as PERT plus or minus three. The resulting ranges are 4.00 to 9.33 weeks and 2.67 to 10.67 weeks. These percentages come from the normal curve; a single activity can be skewed, so treat the bands as planning approximations rather than promises.

Notice what the example says. The likely plan is near seven weeks, but the eight-week O–P spread is not a detail to hide. It may reflect approval uncertainty, technical discovery, supplier lead time or the chance of rework. The range gives a sponsor a better question than “What is the date?”: “Which assumption would move us toward the outer band, and what response is worth funding?”

How to choose O, M and P responsibly

Optimistic is the shortest credible outcome if known positive conditions hold. It is not a target created by asking the team to work harder. State what must be true: the environment is ready, decisions arrive on time, the familiar approach works and no material rework appears. Pessimistic is a defensible downside in which identified risks materialise or the work reveals complexity the team can reasonably foresee. An unlimited catastrophe belongs in a separate scenario, not in every P value.

Most likely should represent the current plan and evidence, not an executive target. Look at similar completed work, cycle time, supplier lead times and design maturity. Ask what would have to be true for M to be wrong. If different experts choose very different points, keep that disagreement visible. A wide range may mean genuine uncertainty, weak scope definition or an unresolved method decision. Do not narrow it simply to make a business case look more certain.

Using confidence ranges in decisions

Match the confidence level to the consequence of being wrong. A 68% band may support an internal conversation or early feasibility view. A 95% band may be appropriate for a funded plan with contingency. A hard external deadline may require a wider allowance, explicit reserve and a response plan. More confidence is not free: it may require more time, more capacity, less scope or a later commitment.

A confidence range is conditional on the inputs, the chosen distribution and stable scope. If the team adds features after the estimate, an actual result outside the original range does not automatically disprove the method. Record the estimate version, date, estimator, scope and assumptions. Revisit it when evidence changes rather than quietly replacing history.

Rolling uncertainty up a path

For a sequence of activities, calculate each activity’s standard deviation, square it to obtain variance, add the variances and take the square root. If three tasks have standard deviations of 1, 2 and 3 days, the path standard deviation is √(1² + 2² + 3²) = √14, about 3.74 days. Naively adding them gives 6 days and overstates the path uncertainty under the independence assumption.

Independence is a modelling assumption, not a fact. A common supplier, shared approval or one design decision can affect several activities together. Correlated risks make the simple square-root roll-up too optimistic. Use a common scenario, dependency analysis or a more advanced simulation when correlation is material. The related path calculator on the desk shows why standard deviations should not be pasted onto every task and then added again.

Common mistakes

• Using M as O. Optimistic must be better than normal or the range understates upside.
• Making P impossible. A disaster with no credible boundary cannot guide a plan.
• Adding standard deviations. Add variances for independent activities, then take the square root.
• Reading 95% as certainty. The band is conditional and approximate.
• Mixing units or scope. A changed boundary requires a fresh three-point estimate.

Make the estimate useful after the workshop

Keep O, M, P, the date, the source of evidence and the main assumptions with the result. When the work finishes, compare actual performance with the range and ask which assumption moved. If supplier lead time caused the miss, improve that input next time. If results cluster near O, M may be conservative; if they cluster near P, the risk response or definition of done may need attention.

For a formal question, apply the named formula and keep the four-times weight on M. For a live project, use the calculator to make uncertainty discussable, then pair the output with a dependency review and an owner for the largest unknown. A defensible estimate is not the one with the smallest range. It is the one whose range tells decision-makers what could move, how much it could move and what they can do about it.