Use for a confirmed contract price, committed quantity, or other certain input.
Monte Carlo Risk Simulation
Model uncertainty, explore possible outcomes, and quantify decision risk.
Use probability distributions to represent uncertain inputs, simulate thousands of scenarios, and estimate the likelihood of achieving a target.
Risk analysis
Probability modelling
Expert estimates
Outcome driver analysis
Browser-based
No data upload required
All calculations are performed locally in your browser.
Why use this tool?
Decision Supported
Use this tool when a decision depends on uncertain values such as demand, cost, duration, lead time, or expert estimates.
What It Tells You
It estimates the distribution of possible outcomes, probability of meeting a target, percentile ranges, and the variables most related to the result.
Example Input
The default profit-target example uses triangular price and cost estimates, normal demand uncertainty, and a fixed-cost range.
Sample Output Interpretation
The result explains target probability, median outcome, plausible range, main uncertainty driver, and whether target risk appears lower, moderate, or higher.
- 1 Choose Model Select a practical risk model
- 2 Define Inputs Set uncertain variables and ranges
- 3 Set Target Configure the target and simulation
- 4 Run Analysis Simulate possible outcomes
- 5 Interpret Results Review risk, ranges, and key drivers
1. Choose Model
Choose a practical sample model, load it, then adapt its assumptions to your decision.
Test whether uncertain demand, price, and cost can achieve a defined profit target.
Illustrative starting point: Review every distribution, parameter, formula, and target before using the result for a real decision.
Your model inputs and simulation results remain in your browser and are not uploaded to a server.
2. Define Inputs
Choose distributions for uncertain inputs. Triangular distributions can be useful when experts can provide minimum, most likely, and maximum estimates.
How to choose a distribution
Use when values inside a credible range are considered equally plausible.
Useful for structured expert estimates when limited observations are available.
Use for approximately symmetric variation around an average; add bounds when negative values are impossible.
Use for positive, right-skewed values such as some costs, durations, and lead times.
Use when only specific events or scenarios can occur.
3. Set Decision Target
Define the result you need to achieve and how many scenarios to test.
Advanced settings
Use these controls when you need to change output formatting, reproducibility, percentile range, or calculation logic.
Insert variable
Supported content: registered variables, numbers, +, -, *, /, and parentheses. JavaScript execution is not allowed.
4. Run Analysis
Simulation runs locally in your browser and uses background processing where supported.
0%
Ready to run the selected sample model.
About Monte Carlo Simulation
Monte Carlo simulation represents uncertain inputs with probability distributions and repeatedly calculates the model to create a range of possible outcomes. It helps decision-makers examine target probability, downside exposure, planning percentiles, and the assumptions most closely related to the result.
The method is useful when one deterministic estimate would hide meaningful uncertainty in demand, cost, duration, inventory, price, or other decision inputs.
Guidance
Start With Evidence
Use historical observations, supplier information, published evidence, or validated business assumptions wherever they are available.
Use Expert Estimates Carefully
When data is limited, document who supplied the estimate and why the minimum, most likely, and maximum values are credible.
Review Planning Percentiles
For cost and lead-time outcomes, higher percentiles can support conservative planning. For profit or remaining inventory, lower percentiles may better represent downside exposure.
Test the Main Driver
Review the strongest input-output relationship, challenge that assumption, and compare scenarios before making the final decision.
Methodology, Assumptions, and Limitations
Formula Logic
Simulation outcome
For iteration r, sample each uncertain input xjr from its selected distribution and calculate yr = f(x1r, ..., xkr)
Uniform sample
x = a + u(b - a), where u is a seeded random value from 0 to 1
Triangular sample
Uses minimum a, most likely value c, maximum b, and inverse-transform sampling on the two sides of the mode
Normal and lognormal
Normal samples use mean μ and standard deviation σ; lognormal samples use exp(Z) where Z is sampled from the specified underlying normal distribution
Fixed and discrete samples
A fixed input returns its stated value. A discrete input selects one listed value according to its normalised probability weight.
Sample mean
ȳ = (1 / N) ∑r=1N yr
Percentile
Pp is the interpolated value at position p(N - 1) in the sorted simulated outcomes
Target probability
Pr(target met) = count of simulated outcomes meeting the target / N
Driver correlation
rxy = cov(x, y) / (σxσy), used to screen linear input-outcome relationships
The seed makes an unchanged sample scenario reproducible. Correlation ranks association, not causation, and may understate nonlinear or interaction effects.
Assumptions
The selected distributions, parameters, formula, target, and independence between variables are assumed to represent the decision adequately.
Limitations
Results depend on input quality. Correlated variables, distribution fitting, Latin hypercube sampling, and nonlinear sensitivity measures are not currently supported.
FAQ
How many iterations should I use?
Start with 10,000 iterations for practical analysis. Increase the count when the output remains unstable or when tail percentiles are important, while recognising that more iterations do not correct weak input assumptions.
Which distribution should I choose?
Choose a distribution that matches the available evidence and the shape of the uncertainty. Use the distribution helper above the inputs and document the reason for each choice.
What does P90 mean?
P90 is the value at or below which 90% of simulated outcomes fall. For cost or lead-time outcomes it can be a conservative planning value; for profit, a lower percentile such as P10 may better describe downside exposure.
Is the driver analysis a sensitivity analysis?
The tool currently uses Pearson correlation to rank linear relationships between sampled inputs and the simulated outcome. It is a useful driver screen, but it is not a complete global sensitivity analysis.
Are my inputs uploaded?
No. The current simulation, scenario comparison, and exports are processed locally in your browser.