Three Point Estimate Formula: PERT Calculator and Programme Roll-Up

• The PERT expected value is (optimistic + 4 × most likely + pessimistic) ÷ 6, and its standard deviation is (pessimistic − optimistic) ÷ 6.
• For a programme total, add the expected values, add the variances (each standard deviation squared), then take the square root of the summed variances. Adding standard deviations overstated our example's spread about 2.1 times.
• Quote the P80 figure, the 80th-percentile total you have an 80% chance of not exceeding (expected total plus 0.84 standard deviations), as the commitment. In our example the sum of the five most likely values was reached or beaten in only 13.9% of simulated outcomes.
• The method assumes independent components and honest inputs. Shared contractors, merging schedule paths and optimistic estimators all push the real spread beyond what the formula shows.

Two formulas share the name. The PERT (Program Evaluation and Review Technique) version divides by 6 and weights the most likely figure four times: (O + 4M + P) ÷ 6. The triangular version divides by 3 and weights all three equally: (O + M + P) ÷ 3. Both are set out in the Wikipedia entry on three-point estimation.

Take a drainage package with a best case of ₹10 crore, a most likely cost of ₹14 crore and a worst case of ₹24 crore. PERT gives (10 + 56 + 24) ÷ 6 = ₹15.0 crore. Triangular gives (10 + 14 + 24) ÷ 3 = ₹16.0 crore.

The gap is wider than it looks. We simulated both shapes with 1,000,000 draws each from 10, 14 and 24 (our model, run in Python (NumPy) in November 2026). For PERT we used a Beta distribution scaled to run from O to P, with α = 1 + 4(M−O)÷(P−O) and β = 1 + 4(P−M)÷(P−O). For the other we used a triangular distribution. The 80th-percentile cost was ₹17.2 crore under PERT and ₹18.7 crore under triangular. The chance of finishing at or below the ₹14 crore most likely figure was 39% under PERT and 29% under triangular.

Our recommendation: use PERT when the people estimating can defend the most likely figure from comparable work. Use triangular when the most likely figure is a hunch and the worst case is the part you believe, because it leans further towards the tail.

Enter three numbers in the same unit, then apply three formulas. The expected value is the weighted average, the standard deviation is one sixth of the range, and the variance is the standard deviation squared. These are the standard PERT formulas, set out in Malcolm, Roseboom, Clark and Fazar (1959), where PERT originated, and summarised in the Wikipedia entry on three-point estimation.

Read it this way: plan on ₹15.0 crore, and expect the outcome to fall between ₹12.7 and ₹17.3 crore (one standard deviation either side) about two times in three, if the outcomes follow a bell-shaped spread. The first half of that sentence is the useful part. The second half is an approximation.

The SD formula is a shortcut. In our 1,000,000-draw simulation of 10, 14 and 24, the true SD was 2.53, not 2.33. For a very skewed case of 10, 12 and 60, the formula gives 8.33 and the simulated SD is 7.45. The error runs both ways, so treat the SD as a good guide, not a measurement.

Add the expected values, add the variances, and take the square root of the summed variances. Do not add the standard deviations. Here are five components of a programme, in ₹ crore, with each row worked from the formulas above.

The programme SD is √24.56 = ₹4.96 crore. To rebuild this in Excel, put O, M and P in columns B to D, rows 2 to 6, and use:

E2:  =(B2+4*C2+D2)/6
F2:  =(D2-B2)/6
G2:  =F2^2
E7:  =SUM(E2:E6)
G7:  =SUM(G2:G6)
F7:  =SQRT(G7)
P80: =E7+0.84*F7
P90: =E7+1.28*F7

Copy row 2's formulas down to row 6. The programme row is the only place where the square root appears. For how this total sits inside tranches and approval gates, see our guide to programme financial management.

Standard deviations do not add because components rarely go wrong together. For independent components, it is the variances that add, and the spread of the total is the square root of the summed variances. Adding standard deviations quietly assumes every component hits its bad case at the same moment.

In the table above, adding the five SDs gives 1.33 + 2.67 + 3.33 + 1.67 + 1.33 = 10.33. The correct figure is 4.96. The wrong method overstates the spread by a factor of 10.33 ÷ 4.96 = 2.1, so the programme looks twice as risky as it is, and the contingency is padded to match.

We checked the correct figure by simulation (our model: Beta-PERT shapes as defined above, 400,000 trials, components independent, run in Python (NumPy) in November 2026). The simulated programme mean was 77.66 and the SD was 5.22, close to the formula's 77.67 and 4.96.

Add a multiple of the programme SD to the expected total. For the P80 figure, the 80th-percentile total you have an 80% chance of not exceeding, add 0.84 SDs. For P90, the total you have a 90% chance of not exceeding, add 1.28. These multiples come from the standard normal curve, and they hold when the total is roughly bell-shaped, which sums of several components tend to be.

The last row of the table shows why single-point budgets disappoint. Adding the five most likely figures gives ₹72 crore, yet only 13.9% of our 400,000 simulated outcomes came in at or below it.

Our recommendation: take P80 (₹81.84 crore here) as the commitment to the sponsor. That is ₹4.17 crore above the expected value. Take P90 where overruns are penalised, such as fixed-price commitments. Show the expected value alongside, so the sponsor sees the contingency as a visible line.

For where such a contingency belongs in the risk record, see our RAID (risks, assumptions, issues, dependencies) log guide and our guide to programme risk management.

It stops being reliable when its inputs are optimistic, when components move together, and when schedule paths merge. The formula cannot repair any of these: the accuracy of the results can be no better than the accuracy of the three initial points (Wikipedia).

• Optimistic inputs. In its April 2026 Flash Report, India's Ministry of Statistics and Programme Implementation (MoSPI) tracked 1,981 ongoing central-sector infrastructure projects costing ₹150 crore and over. Scope changes explain part of that, so it is not a pure estimating error.
• Slipping dates. This is our count from the report's project table.
• Shared drivers. The roll-up assumes components are independent. If all five depend on one contractor, one clearance or one monsoon season, the true spread lies between 4.96 and 10.33 (perfect correlation makes the SDs add). We would use the upper end for shared-driver components.
• Merging schedule paths. This applies to durations, not costs. Read the same five estimates as weeks. One path has an expected length of 77.67. With three equal, independent parallel paths, the longest one averaged 82.17 in our simulation, 4.50 weeks (5.8%) longer. Planning off a single path understates the date.
• The range-over-six shortcut. A June 2026 preprint on meta-analysis (arXiv 2606.17424) shows that standard deviations estimated from three-number summaries are unreliable without shape information. It has not been peer reviewed.

Run these four tests before you publish a range:

1. Is each worst case defensible? Pass: P has a written cause (for example, "clearance slips two quarters"). Fail: P is simply M plus 10%.
2. Did the people doing the work supply O, M and P? Pass: they did, using one shared definition of "most likely". Fail: one person estimated every component.
3. Do components share a driver? Pass: none do, or you also report the wider 10.33-style bound. Fail: the same contractor or approval sits behind several rows and you reported only the root-sum-of-squares figure.
4. Are all estimates at one price date? Pass: every row uses the same base month. Fail: rows mix quotations from different dates.

For the economics of the programme the estimates feed, see our programme business case guide, and for tracking spend against plan, our earned value formula worked example.

Rolling up estimates is a core programme-management skill: it produces the sponsor's number, the contingency and the gate decisions. We teach programme and portfolio management, and we prepare candidates for the Project Management Institute (PMI) PgMP® (Program Management Professional) and PfMP® (Portfolio Management Professional) certifications, though PMI awards them, not us.

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