Monte Carlo simulation propagates uncertainty through a formula by drawing each input from its own distribution thousands of times and reporting the distribution of the result.
When a quantity is computed from several uncertain inputs, the uncertainty of the result rarely has a closed form. The usual alternative — first-order propagation, adding partial derivatives in quadrature — assumes the model is near-linear over the range of the inputs and that the result is roughly normal. Simulation assumes neither: it just evaluates the model many times and looks at what comes out.
This is the method GUM Supplement 1 specifies for measurement uncertainty when the linear approximation is not safe, and the same machinery answers risk questions outside metrology — a cost built from uncertain components, a yield built from uncertain rates.
A seeded run is exactly reproducible. An unseeded one reports the seed it drew, so any result can be reproduced after the fact.
A model written as an expression, plus a distribution for each named input. Operators + - * / ^ and sqrt, exp, ln, log10, abs, min and max are available.
The mean, SD, median, range and a coverage interval for the simulated output, with the seed used.