Determine how many Monte Carlo iterations are needed for a target precision.
Monte Carlo error falls with the square root of iterations, so halving the error requires four times the runs. That square-root convergence is the fundamental cost of simulation. Variance reduction techniques such as antithetic variates or importance sampling improve precision far more cheaply than simply running more iterations.
Monte Carlo Sample Size
n = (z σ ÷ precision)²
n = (z σ ÷ precision)² Monte Carlo error falls with the square root of iterations, so halving the error requires four times the runs. That square-root convergence is the fundamental cost of simulation.
Variance reduction techniques such as antithetic variates or importance sampling improve precision far more cheaply than simply running more iterations.
This calculator takes 4 inputs: Standard deviation of the output, Desired precision of the mean, Confidence level, Seconds per iteration. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.