Poisson Probability Calculator
Compute the Poisson probability of k events.
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Introduction
Poisson Probability Calculator — Compute the Poisson probability of k events. Enter Rate (λ), Occurrences (k) to get an instant, accurate result.
Formula
Poisson PMF: P(X=k) = (λᵏ × e⁻λ) / k!, the probability of k events occurring when the average rate is λ events per interval.
Step-by-step
- Enter the Rate (λ).
- Enter the Occurrences (k).
- Click Calculate to see your result instantly.
Real-world example
Example: With Rate (λ) = 4, Occurrences (k) = 2, the Poisson Probability Calculator gives Probability: 0.1465.
Frequently Asked Questions
When is the Poisson distribution appropriate?
It models the count of independent, rare events happening at a constant average rate over a fixed interval of time or space, such as calls arriving at a call center.
How does λ relate to the mean and variance?
For a Poisson distribution, both the mean and the variance equal λ.
What inputs does the Poisson Probability Calculator need?
You'll need to provide: Rate (λ), Occurrences (k). All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.
How accurate is the Poisson Probability Calculator?
The Poisson Probability Calculator applies the formula exactly as calculated — Poisson PMF: P(X=k) = (λᵏ × e⁻λ) / k!, the probability of k events occurring when the average rate is λ events per interval. — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.
Is the Poisson Probability Calculator free to use?
Yes, the Poisson Probability Calculator is completely free, requires no signup, and runs instantly in your browser.
About the Poisson Probability Calculator
The Poisson Probability Calculator uses a real, verifiable formula — Poisson PMF: P(X=k) = (λᵏ × e⁻λ) / k!, the probability of k events occurring when the average rate is λ events per interval. — so results are accurate every time, not an approximation.