Monte Carlo simulator
Give a range instead of a single number. Describe each input's uncertainty (low, likely, high), pick a model template, and the tool runs tens of thousands of random scenarios to show the distribution of the result, its likely range and the probability of beating a target.
Inputs
Input A
Input B
Input C
From 100 to 200,000. A larger N reduces the random error of the mean.
With the same seed and the same inputs the result repeats exactly. An integer from 0 to 4,294,967,295.
Calculates the probability that the result exceeds this value (e.g. a budget or profit target).
The simulation runs in your browser; your inputs are not sent anywhere.
To turn uncertainty into a decision, let us build your model on your real data and validate it together.
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How to use
A
Pick a model template and enter the distribution and its parameters for each input (if unsure, use a triangular distribution with minimum, likely and maximum), or load the example model.
B
Optionally enter a target value, set the number of runs and the seed, and run the simulation.
C
Read the mean, the P5/P50/P95 range, the probability of exceeding the target and the histogram and cumulative charts; copy the result.
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How does a Monte Carlo simulation work?
In each run every input draws a random value from its own distribution, the values are combined by the model template and one result is produced. After tens of thousands of runs the distribution of results shows the range of outcomes the uncertain inputs create together. Instead of one "most likely" scenario you get an answer such as "the probability of reaching the target is 70%".
The random numbers come from a seeded generator (mulberry32): with the same seed and inputs the result is always the same, so the analysis is repeatable. Changing the seed is the practical way to see the size of the random error.
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Choosing a distribution: triangular, normal, uniform
The triangular distribution fits when you can estimate "at least this, most likely that, at most this"; it is common for project duration and cost estimates when data is scarce. The normal distribution suits quantities that are the sum of many small effects and vary symmetrically around a mean (measurement error, demand deviation); it is theoretically unbounded, so negative values can occur.
The uniform distribution is used when you know only the lower and upper limit and consider every value in the range equally likely. Your choice can change the result noticeably; when unsure, run with two distributions and compare the difference.
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How to read the result
P5, P50 and P95 are the values below which 5%, half and 95% of the results fall. The P5–P95 range gives the band in which the result stays with about 90% probability. A gap between median and mean shows a skewed distribution (products tend to skew to the right).
The probability of exceeding the target is the share of runs above it. It is an estimate with a random error that shrinks as N grows. If inputs are really related (for example demand falls as price rises) the independence assumption can mislead.
FAQ
- How many runs are enough?
- For the mean, 10,000 runs are enough for most purposes; extreme percentiles such as P5 and P95 and small probabilities need more. The standard error of the mean is shown as σ/√N; multiplying N by 100 cuts the error to a tenth.
- What does the seed do?
- It is the starting value of the random number generator. With the same seed and the same inputs the result repeats exactly, which keeps an analysis consistent when you share or rerun it. Different seeds give different random samples.
- How should I choose the distribution parameters?
- If you have past data, take the mean and standard deviation from it (normal) or use its lowest, typical and highest values (triangular). Without data use expert judgement; but people usually estimate uncertainty too narrowly, so keep the range a little wide.
- What if the inputs depend on each other?
- The tool assumes independent inputs. Inputs that really move in the same direction (cost items, for example) make the total uncertainty wider than the independence assumption shows; inputs moving in opposite directions make it narrower. With strong dependence a correlated model is needed.
- Why can I not type a free formula?
- For safety and simplicity only four fixed templates are offered (A+B+C, A×B, A×B−C, A×B×C), so no code is evaluated in your browser. For more complex models we can build your model together.
- Is the probability of exceeding the target an exact risk figure?
- No. It is an estimate that depends on the distributions you chose and the independence assumption. If the input estimates are wrong, so is the result. For a decision, run a sensitivity analysis: change the input ranges and see how the probability moves.
Turn uncertainty into decision support
Let us back your cost, duration or demand estimates with real data and turn them into risk and scenario analysis, and find together which input moves the result most.