Monte Carlo simulation

Monte Carlo simulation estimates the range of possible outcomes for a model by running it many times, often thousands or millions, with inputs randomly sampled from a specified probability distribution each time, rather than a single fixed value. The result is not one answer but a distribution of outcomes, showing not just an expected value but how much it could plausibly vary.

This differs from a standard what-if analysis, which typically changes one or a few inputs to fixed alternative values to see specific "what if" outcomes; Monte Carlo instead samples across the full range of uncertainty in every input simultaneously, capturing how those uncertainties compound. It relies on defining a realistic probability distribution for each uncertain input, project duration, demand, investment return, which is often the hardest and most consequential modeling choice.

Monte Carlo simulation matters for financial forecasting, project risk, and capacity planning, anywhere outcomes depend on several uncertain factors at once, and it underlies risk measures such as value at risk. A common pitfall is running too few iterations to get a stable distribution, or feeding in input distributions that understate real-world uncertainty, measured by their standard deviation, or ignore correlation between inputs, which produces a confidently precise-looking result that is not actually reliable.