Poisson Probability
Free Poisson Probability calculator with clear step-by-step results.
About Poisson Probability
The Poisson distribution models rare events in a fixed interval.
Formula
Formula
P(X=k) = e^(−λ)·λ^k / k!
Worked example
With the default values below, Poisson Probability returns P(X = k) of 0.224042. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Mean rate λminimum 0
- 3
- Observed count kaccepts 0–170
- 2
Results
- P(X = k)
- 0.224042
- Std Deviation √λ
- 1.732
- λ Used
- 3.000
Step by step
- 1Values used
- 2Formula
- 3P(X = k)= 0.224042
- 4Std Deviation √λ= 1.732
- 5λ Used= 3.000
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How does this calculator work?
The Poisson distribution models rare events in a fixed interval.
Why does this matter?
Events should occur independently.