Our Poisson distribution calculator helps you quickly determine the probability of a given number of events occurring within a fixed interval of time or space.

## Poisson Distribution Calculator

**How to Use the Calculator**

Enter the mean number of occurrences (λ) and the actual number of occurrences (k) you wish to find the probability for. Then, click the “Calculate” button to get the result.

**How it Calculates the Result**

This calculator uses the Poisson distribution formula:

`P(k; λ) = (λ`^{k} * e^{−λ}) / k!

Where:

**k**is the number of actual occurrences,**λ**is the expected mean number of occurrences,**e**is Euler’s number (approximately equal to 2.71828).

It substitutes your values of λ and k into this formula to compute the result. Division by the factorial of k is done using a simple iterative method, as JavaScript does not have a built-in function for factorials.

**Limitations of the Poisson Distribution Calculator**

The Poisson Distribution is ideal for modelling events with a known average rate of occurrence if these events are independent of each other. It may not be suitable if the events are not independent, or if the interval is non-uniform. Additionally, the calculator operates within the limits of JavaScript’s numerical precision and might not handle extremely large numbers or extremely low probabilities well.