Poisson Probability Calculator
Estimate exactly k events under a constant-rate Poisson model.
Your inputs
Calculation results
Formula & assumptions
P(X=k) = e⁻λ λᵏ/k!; events are assumed independent at a constant rate.
Values use the specified units. Calculations use floating-point arithmetic. Check input measurements and formula assumptions before applying the result.
Compare your scenarios
Save up to five results to compare changes side by side. Scenarios stay in this tab until you clear or reload it.
Using Poisson Probability Calculator
Estimate exactly k events under a constant-rate Poisson model.
- Enter expected events, observed events using the units printed under each field.
- Choose Calculate, or enable live updates. Review the result labels and formula assumptions.
- Save scenarios to compare up to five variations, then copy the report or download JSON or CSV.
Example
Expected events: 4 events Observed events: 2 events Probability · percent: 14.652511 Variance: 4 Standard deviation: 2
Questions & answers
What does Poisson Probability Calculator calculate?
Estimate exactly k events under a constant-rate Poisson model.
Which units should I enter?
Expected events uses events. Observed events uses events. Convert values to these units before calculating.
Which formula does it use?
P(X=k) = e⁻λ λᵏ/k!; events are assumed independent at a constant rate.
What does the included example show?
Expected events: 4 events; Observed events: 2 events. Result: Probability · percent = 14.652511; Variance = 4; Standard deviation = 2.
Can I compare different settings?
Yes. Save a scenario, change the inputs and save another result. Up to five scenarios are compared in this tab; they disappear when you reload or leave.
Can I export the calculation?
Copy the JSON report or download JSON and CSV with inputs, result labels and numeric values. Processing uses local JavaScript; no calculation request is sent to our server. Displayed values use up to 10 significant digits; exports retain JavaScript numeric precision.
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