Poisson Probability Calculator
Evaluate an event-count probability and both cumulative tails for a supplied expected count.
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How to use Poisson Probability Calculator
P(X=k)=exp(−lambda)×lambda^k/k!. Regularized gamma tails evaluate P(X≤k) and P(X>k) separately to retain small tail probabilities.
- Enter expected count lambda, observed count k.
- Check the model, units, and supported limits before calculating.
- Run the tool, inspect the result, then copy or download it.
Good to know
- Expected count 0–1000, integer count 0–10000. Independent constant-rate Poisson model; this does not establish that measured events follow it.
- Runs locally. Numeric inputs are bounded; floating-point output is approximate and rounded to 12 significant digits. Unsupported or non-finite calculations produce an error.
Common questions
How does Poisson Probability Calculator calculate its result?
P(X=k)=exp(−lambda)×lambda^k/k!. Regularized gamma tails evaluate P(X≤k) and P(X>k) separately to retain small tail probabilities.
What assumptions and boundaries apply?
Expected count 0–1000, integer count 0–10000. Independent constant-rate Poisson model; this does not establish that measured events follow it.
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