Monte Carlo Simulation Calculator

Work out monte carlo simulation instantly with clear inputs, formula shown and shareable results.

About Monte Carlo Simulation Calculator

Monte Carlo estimates a probability by the fraction of simulated successes. Its error shrinks as 1/√n, so quadrupling the trials halves the uncertainty — the reason large simulations are needed for high precision.

Formula

Monte Carlo error

SE = √(p(1 − p)/n), so precision improves as 1/√n

Worked example

With the default values below, Monte Carlo Simulation Calculator returns Monte Carlo estimate of 0.25300000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Number of simulated trialsminimum 1: 10,000
True success probabilityaccepts 0.01–99.99 %: 25 %
Observed successesminimum 0: 2,530

Results

Monte Carlo estimate: 0.25300000
Theoretical standard error: 0.0043301270
95% confidence half-width: 0.0085205701
z distance from the true value: 0.692820

Step by step

1Values used
2Monte Carlo error
3Monte Carlo estimate= 0.25300000
4Theoretical standard error= 0.0043301270
595% confidence half-width= 0.0085205701
6z distance from the true value= 0.692820

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 10 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For 2530 successes in 10000 trials with true p = 0.25?

The estimate is 0.253, well within the standard error of 0.00433, giving z ≈ 0.69.

How do I get one more decimal place?

You need roughly 100 times as many trials, since the error falls only as the square root of the count.