P50, P80 and P90: what they mean and which to budget at

Guide · Updated October 2026

P50, P80 and P90 are the values that 50%, 80% and 90% of simulated outcomes stay at or below: in a building project example (USD thousands), the total cost’s P50 is 2,776, its P80 2,879 and its P90 2,937. So a P80 budget is exceeded in one outcome in five, and a P90 budget in one in ten.

Budgeting at P80 here means a contingency of 259 on top of the base estimate of 2,620. Which level to fund is a choice of how often you accept an overrun, and each step up costs more per point of confidence. Take the percentile of the total, not the sum of the parts’ percentiles: the six cost items’ P80s add up to 2,843, but the P80 of the six items’ sum, before risk events, is 2,756.

What P50, P80 and P90 mean

A Monte Carlo simulation recalculates a model thousands of times, each time with random values drawn from the ranges of its uncertain inputs, and records the result of every run. The example on this page is the building project: six cost items, each a PERT distribution from min through most likely to max, and four risk events that may or may not happen, simulated 5,000 times.

Sort the 5,000 total costs from low to high. P80, the 80th percentile, is the value 80% of the way up the list: 80% of outcomes are at or below it and 20% above. So P80 is exceeded in one outcome in five, P90 in one in ten, and P50, the median, splits the outcomes in half. Between two neighboring outcomes the percentile is interpolated along a straight line, the same definition as Excel’s PERCENTILE.INC.

In this run exactly 1,000 of the 5,000 outcomes, 20.0%, cost more than the P80 of 2,879.

P80 is often called the 80% confidence level. It describes the model, not the future: 80% of the outcomes that the ranges and risks you entered can produce. A missing risk or a range drawn too narrow makes every P-level optimistic. And it is not a statistical confidence interval: it says where outcomes fall, not how precisely a number has been estimated.

Watch the direction. On this page and in xellstorm, P90 is the value 90% of outcomes stay at or below: for a cost, the high side. Oil and gas reserve estimates use the opposite convention, where P90 is the quantity with a 90% chance of being exceeded. Check which one a report uses before comparing numbers.

Reading P-levels off an S-curve

An S-curve, or cumulative probability curve, plots each value against the share of outcomes at or below it. To read a P-level, go across from its percentage to the curve, then down to the value: across from 80% gives the P80, 2,879. To read the other way, go up from a value to the curve and across: the chance of staying at or below it. The base estimate, the sum of the most likely costs, is 2,620; it meets the curve at only 5.8%, so it is about the P6, and 94.2% of outcomes cost more.

In xellstorm, hover over the S-curve on the Results step, or tap it on a phone, to read the chance of staying at or below the value under the pointer. The percentile table lists P1, P5, P10, P25, P50, P75, P80, P90, P95 and P99, and the key figures at the top show the P90, or the P10 when higher is better: set under “Good when”, or taken from a target such as “gap < 0.4” or a name such as Profit.

Its P80 row gives the P80 on this page. The probability box below the key figures answers the reverse question: pick <=, type a budget, and it shows the chance of staying at or under it. The results workbook’s Trials sheet lists every trial, so =PERCENTILE.INC on the output’s column gives any other level.

Spread: P90 − P10 and P90 − P50

The distance between two P-levels measures how uncertain the outcome is, in its own units. P10 to P90 holds the middle 80% of outcomes: for the building project, from 2,644 to 2,937, a spread of 293, or 10.5% of the P50. It is the shaded band on the S-curve above.

The two halves need not match. P90 − P50, how far a one-in-ten bad outcome lies beyond the median, is 161 here, while P50 − P10 is 131. Costs can overrun further than they can underrun, so the upper half is the longer one, and a symmetric ± range around the P50 cannot describe it.

Contingency at P50, P80 or P90

Contingency is what you add to the base estimate to reach the chosen P-level: contingency = P-level − base estimate. For the building project, with a base estimate of 2,620:

The P80 contingency, 259, comes to 9.9% of the base estimate. That share is a result of this project’s ranges and risks, not a rule: a project with wider ranges or larger risks needs more, which a flat percentage cannot tell. The same reading works for time, where the P80 finish of this project is week 60.7 (see schedule risk analysis), and for a risk register, where the reserve is the P-level of the total loss itself.

Which level to budget at

No P-level is right for every budget: choosing one is deciding how often you accept an overrun. A P50 budget is exceeded in half of outcomes, a P80 budget in one in five, a P90 budget in one in ten. Some things to weigh:

• Each step up costs more per point. In the building project, going from P50 to P80 adds 103 (USD thousands), or 3.4 per percentage point; from P80 to P90 adds 58, 5.8 per point; and from P90 to P95 adds 47, 9.3 per point. Outcomes thin out toward the tail, so each extra point of confidence reaches further.
• What an overrun costs you, against the cost of holding money back. If going over means a new approval round or a lost margin you cannot recover, a higher level can pay for itself; if an overrun is easy to absorb, a lower one frees money for other uses.
• How many budgets you hold. Over many independent projects, overruns and underruns partly cancel, and the combined cost tends toward the sum of the means, not of the P50s. With costs skewed to the right, as here, the mean (2,785) is above the median (2,776), so P50 budgets fall short on average.
• Where you hold the contingency. Set it on the total, not item by item: adding each item’s P80 overshoots the items and still leaves out the risk events, as the next section shows.
• How good the ranges are. Every P-level is only as good as the ranges and risks that went into the model.

Percentiles do not add up

It is tempting to build a P80 budget from the parts: take each cost item’s P80 and add them up. The result is not the P80 of anything. Here are the six cost items of the building project, with each item’s percentiles and those of their sum read from the same 5,000 trials:

The items’ P80s add up to 2,843, 87 more than the P80 of their sum, 2,756. The sum of the items exceeds 2,843 in only 2.9% of outcomes, so that figure is about their P97, not their P80. Adding P50s errs the other way, 2,675 against 2,687, and the added P10s, 2,477, lie below every one of the 5,000 simulated sums. Only the means add up: 2,692 either way.

For the P80 the reason is that the items vary independently. Adding P80s budgets for every item coming in at its own P80 at the same time, yet with six independent items the chance that all of them land at or above their P80 together is 0.2⁶, one in 15,625. Usually a high item is offset by others near or below their middle, the same effect that makes a worst-case tolerance stack-up so conservative. The added P50s fall short for a different reason: each item’s range reaches further above its most likely cost than below it, and the median of a sum of such skewed items tends to lie above the sum of their medians, closer to the mean. Percentiles are sure to add up only when the parts move in lockstep, each at its own P80 whenever another is.

The risk events make it worse. The project’s total also carries four risk events, which adding the items’ P80s leaves out: 2,843 is 36 below the total’s P80 of 2,879, only about the total’s P71. Adding the risks’ own percentiles does not repair it: Ground conditions, which occurs in 25% of outcomes and then costs 150, has a P50 of 0 and a P80 of its full 150: added P50s count it as never happening, added P80s as always happening. Read the percentile of the total from the simulation. The same goes for a portfolio: the P80 of several projects together is not the sum of their P80s.

Questions

Related

• Project cost and schedule

  How much contingency does a construction project need?

  Worked example: a building estimate’s most likely costs are exceeded in 94.2% of simulated outcomes. Size the construction cost contingency with Monte Carlo.
• Risk management

  How much contingency does a risk register need?

  Probability × likely impact sums to 291; the simulated mean loss is 359 and the worst 5% average 1,436 (USD thousands). Size contingency from the tail.
• Guide

  Schedule risk analysis: why projects finish late

  A building schedule of most likely durations says week 55, yet only 14.3% of simulated outcomes finish by then. Why, and how to set a P80 finish.

xellstorm is a browser-based Monte Carlo simulation tool for Excel models: no add-in, and the workbook never leaves your computer.