Monte Carlo simulation calculator
Choose a model, simulation count and random seed. The calculator shows how a random estimate approaches its theoretical value.
Estimate convergence
The dashed line is the theoretical value. Random variation usually decreases as simulations accumulate.
Simulation checkpoints
| Simulations | Estimate | Absolute error |
|---|---|---|
| Fill in the fields above — the result is computed on this page. | ||
How to use this page
- Choose event probability or pi estimation.
- Set the simulation count and random seed.
- Compare the estimate, error and convergence chart.
What this page does not do: This is an educational browser-based simulation. It does not replace an analytical solution when one exists or a professional risk model.
Further reading
Monte Carlo methods approximate a result through repeated random sampling. The Bernoulli model counts the share of successes. The pi model samples points in a square and measures the share inside a quarter circle.
A random seed makes the example reproducible; it does not change the mathematics of the method.
Frequently asked questions
Why does the result change with the seed?
A different seed creates a different but still reproducible pseudorandom sequence.
How many simulations should I use?
Start with 10,000. Increase N and watch whether the estimate stabilizes; computation time grows linearly.
See also
ACF and PACF autocorrelation calculator
Calculate ACF and PACF across time-series lags. Review the chart, reference bounds and coefficient table.
Adjusted R-squared calculator
Convert R² to adjusted R² using the number of observations and predictors in a regression model.
Beta distribution calculator
Calculate beta density, CDF, upper tail and quantile together with its mean and variance.