Poisson Distribution Calculator

Calculate exact and cumulative Poisson probabilities using event rate λ and number of events k.

Formula:
P(X = k) = (e^-λ · λ^k) / k!

Result will appear here.
Metric Value

Privacy: calculations run locally in your browser. No inputs are stored or transmitted.

How it works

The Poisson distribution models how many events occur in a fixed interval when events happen independently at an average rate λ.

Examples

  • λ = 4, k = 2 → exact probability of exactly 2 events
  • P(X ≤ k) adds all exact probabilities from 0 through k

When to use this tool

This tool is designed for quick, practical tasks such as everyday calculations, data formatting, or simple conversions. It is best used when you need fast results without installing software or using complex tools.

When to use

  • Quick checks or one-time calculations
  • Validating or converting data before using it elsewhere
  • Simple tasks that do not require advanced software

When not to use

  • Critical financial, legal, or medical decisions
  • Large-scale or automated processing
  • Situations requiring guaranteed precision beyond basic validation

Always review results before using them in important contexts.

About this tool

This tool helps you perform quick utility operations directly in your browser. It runs entirely in your browser without sending data to a server.

You can use this tool when handling simple tasks without installing additional software. The results should be interpreted as a processed output based on your input data.

FAQ

  • What does this Poisson calculator compute?

    It computes exact probability P(X = k) and cumulative probability P(X ≤ k) for a Poisson distribution.

  • What is lambda (λ)?

    Lambda is the average rate or expected number of events in the interval.

  • Can lambda be negative?

    No. Lambda must be 0 or greater.

  • Are calculations stored?

    No. Everything runs locally in your browser.

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