✓ Effortless Math · Free Tool

Poisson Distribution Calculator

Find P(X = k) and the cumulative probabilities for a Poisson process with mean λ — plus the mean, variance, standard deviation, and a bar chart.

P(X = k) = e−λ · λk / k!
λ = mean λ ,  k = events k

λ is the average number of events; k is the count whose probability you want (a whole number ≥ 0).

Results

P(X = k)
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P(X = k)
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P(X ≤ k)
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P(X ≥ k)
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P(X < k)
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Mean & Variance
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Std. deviation
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Distribution P(X = i)

Step-by-step