Using the Monte Carlo Method to Estimate the Value of Pi

Application ID: 127901

A classic way of estimating pi is by using the Monte Carlo method. This involves randomly placing points inside a square and counting how many lie within a circle inscribed in the square. The ratio of points inside the circle to the number of points in total can be used to approximate pi, with more points leading to greater accuracy.

This simulation application is created from a model that uses particle tracing to estimate the value of pi with the Monte Carlo method. The app offers the user the ability to vary the number of points, and it provides the estimated value and the error from the true value. In addition, the app helps demonstrate the ease of creating and using apps with the COMSOL Multiphysics® software.

This application example illustrates applications of this type that would nominally be built using the following products: