Poisson Distribution Calculator – Fast & Accurate Probability Results

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) = (λk * e−λ) / k!


  • 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.

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