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SigmaCalc
The distribution behind call-center volume, website traffic spikes, and any 'how many events in this time window' question.
It models the count of independent, rare-ish events over a fixed interval of time or space, where events happen at a known average rate but the exact timing is random — customer arrivals, typos per page, server errors per hour.
λ (lambda) is the average number of events in the same interval you're asking about — if your rate is per hour but you want a probability for a 10-minute window, convert λ to match that window first.
P(X = k)
0.195
P(X = k) = e⁻λ × λᵏ ÷ k!
What you entered
Apply the Poisson formula
P(X = 3) = e^(−4) × 4^3 ÷ 3!= 0.1954Result
P(X = k): 0.195
If events happen at an average rate of 4 per interval, there's a 19.54% chance of seeing exactly 3 in a given interval.