Monte Carlo Simulation Calculator
Run a Monte Carlo simulation on up to three uncertain inputs, each given as a minimum, most likely and maximum — and read off the mean, the P10, P50 and P90, and the chance of clearing a target.
Each input is drawn from a triangular distribution between its minimum and maximum, peaking at the most likely value.
How the monte carlo simulation calculator works
Each input is drawn from a triangular distribution between its minimum and maximum, peaking at the most likely value. The inputs are combined — added or multiplied — thousands of times, and the results sorted.
The P10 and P90 are the numbers to plan with: only one run in ten fell below the P10, and only one in ten rose above the P90. The mean is often not a value that any single run produced.
Formula: each trial: combine(tri(min, mode, max) for each input); read percentiles of the sorted trials
Worked examples
| Inputs | P50 (median) | Note |
|---|---|---|
| Three inputs multiplied | 46,916.36 | a P10-P90 range around 47,000 |
| Two inputs added | 1,137.69 | a narrower, symmetric result |
| More trials | 46,621.85 | the same seed, tighter percentiles |
FAQFrequently asked questions
What is a Monte Carlo simulation?
Drawing every uncertain input at random from its range thousands of times, combining them each time, and reading the spread of results instead of a single number.
What is a triangular distribution?
The simplest shape that uses a minimum, a most-likely and a maximum. It is what a three-point estimate becomes when you have nothing better.
Why is the mean different from the point estimate?
Because multiplying skewed ranges produces a skewed result. The most-likely values combined are not the most likely combination.
Why does the answer not change when I re-run it?
Because the simulation is seeded from your inputs. The same inputs give the same result, which is what makes it reproducible — change an input and the seed changes with it.
How many trials do I need?
A few thousand for the P10 and P90 to settle. Beyond ten thousand the percentiles barely move for a three-input model.
Where these figures come from
- Hubbard (2014) — How to Measure Anything — the case for ranges over point estimates
- Vose (2008) — Risk Analysis: A Quantitative Guide — Monte Carlo and the triangular distribution
- Saltelli et al. (2008) — Global Sensitivity Analysis: The Primer — one-at-a-time sensitivity and its limits
- Standards Australia — AS ISO 31000 Risk management — the Australian standards body
Last checked: September 2026. The methods are textbook decision analysis: triangular distributions for three-point estimates, tornado ranking for sensitivity, and simple additive weighting for decision matrices.