Build the cost estimate as a Monte Carlo model: a distribution on every uncertain line item, each identified risk as an event with its own probability and impact, and correlation between the items that move together. Simulate, and read the distribution of total cost. Contingency is the value at your chosen confidence level minus the base estimate.
On the worked example below, a €12.0m base estimate carries €1.96m of contingency at P80 — the budget level with an 80% chance of not being exceeded. The base estimate itself turns out to sit at only the P18, meaning it would be exceeded in more than four runs out of five. That is the first thing a simulation tells you and a percentage uplift never can.
Cost contingency is the amount added to a base cost estimate to cover identified risks and estimating uncertainty, so that the resulting budget reaches a chosen confidence level. It is calculated from a risk analysis of the specific project — not applied as a flat percentage — and it is spent under the project's own change control as risks materialise.
Sizing contingency is one output of the broader discipline of cost risk analysis — our overview of its methods, models and outputs shows where the calculation on this page fits. Contingency is often confused with management reserve, but the two answer different questions. Contingency covers the known unknowns: the line items whose costs are uncertain and the risk events you have identified and quantified. Management reserve covers the unknown unknowns — work outside the identified scope and risk set — and is typically held and released at a higher authority level. A quantitative cost risk analysis sizes the first; the second is a policy decision.
The traditional shortcut — adding 10% or 15% to every estimate — has an obvious problem: it carries no information about the project it is attached to. A routine repeat project and a first-of-a-kind development get the same allowance, so one is overfunded and the other is set up to fail. A defensible alternative is to derive contingency from a Monte Carlo simulation of the cost estimate itself, and to state the confidence level the budget buys.
A P80 cost estimate is the value that the simulated total project cost stays at or below in 80% of Monte Carlo samples. Funding a project at P80 therefore means accepting roughly a one-in-five chance that the final cost exceeds the budget. P50 is the median — an even chance of coming in under or over — and P90 leaves only a 10% chance of overrun.
These percentiles are read directly off the cumulative distribution of total cost that a simulation produces. That is the crucial difference from a percentage uplift: a percentile states its own risk. "The budget is P80" is a testable claim about overrun probability; "we added 12%" is not. Once the estimate is expressed this way, contingency has a precise definition:
Contingency = cost at the chosen confidence level (e.g. P80) − base estimate
The base estimate here is the deterministic point estimate the project started from — commonly close to the sum of most-likely line-item values. Because cost distributions are usually right-skewed (there are more ways for work to go badly than to go unexpectedly well), the base estimate typically sits below P50, which means a project is more likely than not to exceed a raw base estimate. That asymmetry is exactly what the contingency exists to absorb. Below, reading percentiles off a simulated outcome distribution in ModelRisk — the sliders mark any confidence range directly on the histogram, and every percentile is listed in the statistics panel:
The worked example below, drawn as an S-curve. Contingency is the horizontal distance from the base estimate to the confidence level you fund at.
The calculation is a five-step exercise on top of the cost estimate you already have:
The by-products are as valuable as the number itself. A tornado chart of the simulation shows which uncertainties and risk events drive the spread of total cost — which is the shortlist for risk mitigation. Re-running the model after a mitigation shows exactly how much contingency that action releases:
Everything above is easier to see with numbers attached. What follows is a small capital project — ten line items, two identified risk events — taken through the five steps. The figures are illustrative, but they come from an actual simulation of 400,000 samples rather than from the back of an envelope, and every number quoted below is read off that simulation. The model itself is a free download — every figure below can be checked rather than taken on trust.
The base estimate is the sum of the most likely values: €12.0m. Six of the ten items share a common driver — construction labour productivity and commodity prices — so they are correlated with one another rather than modelled as independent. The mechanical package is already ordered, so its range is narrow.
Two identified risks are not ranges on a line item, because either they happen or they do not. Ground conditions worse than surveyed — a 30% chance, costing €0.4m to €2.5m if it occurs, most likely €0.9m. An approval delay pushing earthworks into winter — a 15% chance, €0.2m to €1.1m, most likely €0.45m. In seven runs out of ten the first risk contributes nothing at all; in the other three it contributes a great deal, and that is exactly the shape a range on a line item cannot produce.
Figures are rounded for display; the percentages are computed from the unrounded simulation output. Because these are Monte Carlo results, the last quoted digit of any difference carries a few thousand euro of sampling noise.
The most useful line in that table is the first one. The base estimate sits at the P18: on its own, before a single euro of contingency, the estimate has roughly a four-in-five chance of being exceeded. Nothing was done wrong to produce that — it is what happens when you add up most likely values across right-skewed items, and it is the reason an unqualified point estimate is not a budget.
It also gives the traditional shortcut a fair test. A flat 10% on this project would have funded it at €13.2m, which the simulation puts at the P58 — a two-in-five chance of overrun, presented as prudence. A flat 15% reaches €13.8m, the P76. Neither figure is absurd; what neither can do is tell you which it is. On a different project with the same base cost and tighter ranges, 10% might buy P90.
Running the identical model with the six common-driver items treated as independent — changing nothing else — gives a P80 of €13.67m and a contingency of €1.67m. The correlation is therefore worth about €0.30m, or 15% of the correct contingency; at P90 it is about €0.43m, or 17%. Only the two risk events move this particular model further, and they are at least visible in the register. Correlation costs nothing to get right, and its absence is invisible in the output — the model still produces a confident S-curve, just a narrower one than the project deserves.
The same model answers a question a percentage uplift cannot. Suppose the team spends €150,000 on additional ground investigation before award, which is judged to cut the probability of the ground-conditions risk from 30% to 8% and to narrow its impact to €0.25m–€1.2m, most likely €0.5m. Re-running the simulation with those inputs gives a P80 of €13.59m. Two different numbers come out of that, and they are worth keeping apart:
Counting the survey itself, the P80 budget falls from €13.96m to €13.74m. Those ratios belong to this illustrative model and are not a general return; what transfers is the method, which is available for every mitigation on the register — model it, re-run, and read how much of the reserve it buys back, and how much of the expected cost goes with it. A tornado chart ranks the candidates before you spend anything on them.
Build this on your own estimate — free 15-day trial
There is no universally correct confidence level, but the choice is not arbitrary either. It turns on two costs that differ from owner to owner: what a euro of overrun costs you beyond the money itself, and what a euro held in reserve and never spent costs you. Those two costs can be written down, and together they give a percentile — the next section does exactly that. What the simulation contributes is honesty about the trade-off: each further point of confidence costs more than the last, because the distribution thins as you move up into the tail — and a right-skewed cost distribution stretches further still.
In practice, P50 is common where a portfolio owner funds many projects and can pool their swings — underruns on some offset overruns on others. P80 is a common single-project funding level where an overrun is painful but survivable, and P90 or higher appears where an overrun is unacceptable and the owner knowingly pays for that protection. The important discipline is to make the choice explicitly, derive it rather than inherit it, and record both the number and the reasoning: a budget with an unstated confidence level cannot be audited, compared or defended later.
A portfolio subtlety follows directly from the mathematics: funding every project at P80 does not give the portfolio an 80% confidence level — it usually overfunds the portfolio, because it is unlikely that many independent projects all land in their bad tails at once. Owners of large portfolios often fund individual projects nearer P50 while holding a central contingency sized on the simulated portfolio distribution. Note that this is a pooling argument about the portfolio, not a statement about any one project: for a portfolio member the confidence level that matters is the one on the central reserve.
Cu is what being a euro short costs you; Co is what holding a euro you never spend costs you. Both are measured over and above the money itself. The confidence level that minimises expected friction is Cu divided by the sum of the two — on the figures worked below, an owner who must fund its own overruns lands near P90, while the same project inside a pooled portfolio is funded near P50 for a different reason: pooling.
P* = Cu ÷ (Cu + Co)
This is the critical fractile — the result that sizes a vendor's morning order of newspapers — and it applies to contingency for the same reason: you commit to a quantity before you know how much of it you will need. The derivation takes one line. Suppose the budget is set at B, and you consider adding one more euro to it. That euro costs you Co whenever the project comes in below B, which happens with probability F(B); it saves you Cu whenever the project comes in above B, which happens with probability 1 − F(B). Keep adding euros while the saving beats the cost, and stop where the two balance:
Co × F(B) = Cu × (1 − F(B)) → F(B) = Cu ÷ (Cu + Co)
F(B) is the confidence level — the height on the S-curve at which the budget sits. So the percentile is not simply a matter of taste: it is anchored to the ratio of two costs the owner already has opinions about. One assumption is worth stating, because it is doing real work: the derivation trades the two frictions at their expected value. An owner for whom a single large overrun would be existential rather than merely expensive is not indifferent in that way and will sit higher than the formula says. Risk appetite is not abolished here — it moves out of the percentile and into Cu and Co, where it can be examined and argued with.
Both costs are per euro, and both are measured over and above the money itself. Being a euro short does not usually mean the euro is never spent; it means it arrives late, or expensively, or that something funded is given up instead. Holding a euro in reserve does not mean losing it; it means paying to have it stand by. Only the ratio enters the formula, so the two need to be on the same footing rather than exactly right.
Because only the ratio matters, the formula can be read backwards. Every confidence level is a statement about how much more a euro short hurts than a euro idle — and reading it that way is the fastest test of an inherited number.
Use it in either direction: divide your two costs to get the percentile you should hold, or take the percentile you have inherited and ask whether the ratio behind it is one you would defend out loud. A team that funds at P95 out of caution is asserting nineteen to one — a strong claim, and worth saying aloud before it is adopted as policy. The exception is a percentile driven by a step cost rather than a ratio, which the reverse reading does not describe; see Where the formula stops being reliable below.
The figures below are illustrative; substitute your own. Take a single €100m estimate and put it in front of two different owners.
Same estimate, same S-curve, two different correct answers. Where you sit on the curve is a property of the owner; the curve itself is a property of the estimate — which is why a percentile borrowed from another industry's guidance note is a starting point rather than an answer.
Two footnotes on that table, because it is tidier than reality. Owner B's P50 does not really come out of the formula: whenever Cu and Co are of the same order the answer sits near P50 regardless of their common value — and near P50 the percentile is at its most sensitive to the ratio, so it is the last place to lean on it. What does the work for B is the portfolio argument above: the central reserve is sized on the simulated portfolio distribution, and that is where the confidence level actually bites. Because both of B's costs are small in absolute terms, sitting a few points either side of P50 costs this owner little either way. And notice what owner A's figures say about the habit: P80 asserts a ratio of four to one, while an owner with no route to more money may well be claiming a good deal more than that — worth checking rather than assuming.
The two owners above, plotted. Each curve is that owner’s expected friction cost at every funding level, relative to the best it could do. The minima fall at P91 and P50 — exactly where Cu ÷ (Cu + Co) says they should — and the bottoms are broad, which is why the answer tolerates a rough ratio.
It prices the next euro, so it needs both costs to scale. Where the cost of being short is a step rather than a slope — the covenant that trips, the statutory cap, the approval that would not be granted twice — the formula's answer is a floor and the right one is higher. That is where genuine P95 funding comes from, and it is not derived from this ratio: it comes from putting the threshold into the simulation and looking at the probability of crossing it.
Cu and Co are estimates too. Only their ratio enters, and the percentile moves slowly with it: a factor of one and a half in either direction turns a P80 into a P73 or a P86. In money that is not nothing — on a typical cost curve the contingency at P86 runs to roughly 1.3 to 2 times the contingency at P73, depending on where the base estimate sits — but it is a bounded difference you can argue about explicitly, which is more than can be said for a percentile taken on faith.
A reserve tends to get spent because it exists. The formula holds the cost distribution fixed while it moves the budget, and in an organisation where contingency is treated as an allowance that is not quite true. Where the effect is real, Co is higher than the cost of capital alone suggests — but the useful response is to tighten the drawdown rules, not to fund lower and hope.
A percentile only means something on a curve you believe. Deriving the confidence level is the second half of the job; the first half is a model with honest ranges and real correlation between line items. P90 read off an estimate built from ±10% ranges and independent line items can easily be a smaller and weaker number than P50 read off an honest one. Fix the model first, then choose where to sit on it.
Whichever number comes out, record the reasoning beside it. "The budget is P80" is an assertion; "the budget is P80, because a euro of overrun costs us about four times in friction what a euro of idle reserve costs us, and here is the working" is an argument — and an argument is what survives an audit, a change of sponsor and a challenge from finance.
P50, P80 and P90 are percentiles of the same simulated total-cost distribution — the values that final cost stays at or below in 50%, 80% and 90% of Monte Carlo samples. They differ only in the overrun risk that remains: roughly 50%, 20% and 10%. Report the base estimate together with at least two percentiles, so the reader sees both the middle of the distribution and the price of confidence.
The steps between them are not equal. Confidence gets dearer the further into the tail you go, because the distribution thins above the middle — and a right-skewed cost distribution stretches further still. On a typical cost curve the thirty points from P50 to P80 cost less per point than the ten from P80 to P90, by something between half again and double; the five points from P90 to P95 are dearer still. Which is why the funding percentile is a real decision about the two costs above rather than a technicality, and why "just use P90 to be safe" is an expensive default.
On reporting: a single number is not an estimate — it is a point with no stated risk. The useful minimum is the base estimate, P50 and the chosen funding percentile, each labelled. The gap between P50 and P80 is itself information: it measures the spread of the estimate, so a wide gap tells the reader the estimate is immature or the project genuinely risky before any discussion starts. A common governance pattern reports P50 as the working target the team manages to, and P80 as the approved budget — the difference between the two being the contingency held above the target.
A tempting shortcut is to take a conservative value — say the P80 — of every line item and add them up. The result is not the P80 of anything. For all of the line items to sit at their own 80th percentiles at once would take a run of bad luck, so against the line-item total the sum lands above the 80th percentile — and nobody can say how far above without simulating.
Percentiles simply do not add. This is the core reason a confidence level has to be read off the total cost distribution rather than assembled from the parts. Monte Carlo simulation is the general-purpose way to produce that distribution for a cost breakdown with mixed distributions, discrete risk events and correlation between items; for some narrower structures there are analytical routes to the same total. The same error in the other direction — summing most-likely values — is why base estimates understate the middle of the distribution in the first place: adding the peaks of right-skewed distributions lands below the mean of the total.
The ten line items of the worked example, risk events excluded so the two values are comparable. Adding the ten line-item P80s gives €13.77m — the P87 of that total, not its P80.
The worked example puts numbers on it, and they cut both ways. Adding the ten line-item P80s gives €13.77m, while the simulated P80 of those same ten items is €13.44m: against the line-item total the sum is really the P87. Model those items as independent instead and the same sum of P80s becomes almost the P99 — so how conservative the shortcut is depends entirely on a correlation structure it never looks at.
And it is not reliably conservative at all. Against the project distribution — the ten items plus the two risk events — that same €13.77m is only the P75, which is €0.2m below the P80 budget of €13.96m, because adding line-item percentiles takes no account of discrete risks sitting on top. Summing percentiles produces a number whose confidence level you cannot know without simulating, and which can land on either side of the one you wanted.
The practical rule: estimate uncertainty at the line-item level, but read confidence levels only at the total level, from the simulated distribution.
Published practice runs from P50 to P95, and at least one major regime abandoned percentiles altogether. The spread is worth knowing, partly because it is a reasonableness check on your own number and partly because it settles the argument that any one of them is the standard. They are all reading the same kind of curve; they differ in what an overrun costs the owner.
Two things stand out. The first is that the range is enormous for what is nominally the same calculation — and the Danish case shows what a flat percentage cannot do, which is tell a conservative estimate from a risky one. The second is Norway's split: a high frame for the funder and a central target for the delivery team is a deliberate piece of design rather than an inherited habit, and it is the only regime in the list that visibly designs the gap between the funding level and the delivery target rather than inheriting a single number — though where the 85 itself came from is no better derived than the rest.
Many cost engineers work to the recommended practices of AACE International (the Association for the Advancement of Cost Engineering), and simulation is not an alternative to them — it is the rigorous end of the same family. 44R-08 covers risk analysis and contingency determination using expected value; 119R-21 determines cost estimate accuracy ranges and contingency from tables derived from parametric risk models; 113R-20 combines parametric and expected-value methods for integrated cost and schedule risk. The tabular route is quick, risk-driven and well suited to early estimate classes, and 119R-21 states its own purpose plainly: to "provide a quick, but risk-driven risk quantification method for project evaluation situations where more rigorous risk quantification methods are not justified or possible such as early in the project development cycle or for lower capex projects." (AACE International RP 119R-21, Rev. 28 November 2022 — retrieved 5 Sep 2026.)
That sentence is also the case for simulating. Where a more rigorous method is justified — a large project, a contested estimate, a funding decision that has to survive review — a Monte Carlo model of the project's own cost breakdown does what a table derived from an industry sample cannot: it uses your line items, your ranges, your identified risks and your correlations, and it tells you which of them is driving the number. In practice the two work well together: the parametric tables are an excellent sanity check on a simulated result, and a simulated result that sits far outside them is worth explaining before it is approved.
Ignoring correlation. One of the most consequential errors. Treating line items as independent lets their variations cancel, narrowing the simulated total and shrinking the calculated contingency — precisely when common drivers (market prices, productivity, weather, design maturity) mean the items would actually move together. If the simulated spread looks implausibly tight, missing correlation is the first suspect.
Ranges that are too narrow. Estimators anchor on the base value and offer ±10% out of habit. Historical outturns are the antidote: compare past estimates with final costs and let the observed spread calibrate the ranges. Double counting is the opposite failure — the same risk appearing both as a widened line-item range and as a separate risk event, inflating the tail.
Confusing uncertainty with risk events. Folding a discrete risk ("the permit might be refused") into a line-item range hides its all-or-nothing character; the simulation then never shows the distinct cluster of expensive outcomes that the event actually creates. And finally, presenting a single number without its confidence level — a contingency is only meaningful together with the percentile it was read from and the model that produced it.
Cost estimates usually live in Excel already, and a Monte Carlo add-in turns the estimate itself into the risk model — no re-platforming, and the model remains a readable workbook the estimating team can audit. ModelRisk provides the pieces this article describes: distributions to express line-item ranges, the VoseRiskEvent function to model discrete risk events with their probability and impact, copulas — the mechanism that imposes a realistic correlation pattern across cost items without distorting the shape of each item's own distribution, and simulation results that report any percentile of total cost directly — with tornado charts to show which inputs drive the contingency.
Worked cost models are available to take apart and adapt, starting with this page's own worked example (ten correlated line items, two risk events, the correlation switch), and including the cost of building a house and a development cost estimation model, alongside the full example-model library. ModelRisk costs at most €1,550 per user per year, and the fully functional 15-day free trial is enough to build and simulate a first contingency model on your own estimate. If the estimate exists only as a written brief or a set of notes, ModelRisk MCP — a connector built on the Model Context Protocol — lets an AI assistant build a first version of the model in the workbook for you to check and correct. For contingency on project schedules rather than costs, see Tamara, our schedule risk analysis tool.
Cost contingency is the amount added to a base cost estimate to cover identified risks and estimating uncertainty, so the budget reaches a chosen confidence level. It is calculated from a risk analysis of the specific project, and it is distinct from management reserve, which covers unforeseeable scope.
A P80 estimate is the value that the simulated total cost stays at or below in 80% of Monte Carlo samples — funding at P80 accepts roughly a 20% chance of overrun. P50 is the median: an even chance of coming in under or over.
Build the estimate as a Monte Carlo model: distributions for uncertain line items, risk events with probability and impact, correlation between items that move together. Simulate, read the P80 of total cost, and subtract the base estimate.
Because independent items cancel each other out and correlated ones do not. If steel, labour and productivity all move with the same market, a bad year moves several line items together instead of some up and some down, so the total has a fatter tail. In the worked example above, treating six correlated items as independent understates the P80 contingency by €295,000 — 15% of the correct figure.
Contingency covers identified risks and quantified uncertainty within approved scope and comes out of the quantitative risk model. Management reserve covers unforeseen work outside the identified risk set and is typically controlled at a higher authority level.
They are percentiles of the same simulated total-cost distribution: the values that final cost stays at or below in 50%, 80% and 90% of Monte Carlo samples, leaving roughly a 50%, 20% or 10% chance of overrun. Because the distribution thins as you move up into the tail, each further point of confidence costs more than the last: the ten points from P80 to P90 typically cost between half again and twice as much per point as the thirty from P50 to P80.
Yes — the critical fractile. Hold the percentile Cu ÷ (Cu + Co), where Cu is what being a euro short costs you beyond the money itself and Co is what holding a euro of reserve you never spend costs you over the years it stands committed. A 4:1 ratio gives P80, 9:1 gives P90, 1:1 gives P50. It assumes both costs scale with the amount, so where a shortfall triggers a fixed penalty the answer it gives is a floor rather than the answer.
There is no defensible flat percentage applied without reference to the estimate's own risk profile — the right contingency depends on the uncertainty and risk exposure of the specific estimate. Two projects with the same base cost can justifiably carry very different contingencies at the same confidence level. In the worked example on this page a P80 budget needs 16.4%, while a flat 10% would have funded the same project at only the P58.
Turn your cost estimate into a defensible P80 budget: distributions, risk events, correlation and full simulation results inside the workbook you already have.