Poisson probability calculator

Calculate exact-count probability with your own figures.

Your numbers

Use the units shown. Results update as you change valid inputs.

Use exact-count probability to compare changes to your inputs. The method and limits below explain the scope.

Examples

Examples

Try the starting example

Mean count
2
Observed count
0
Exact-count probability
0.135335

Try another scenario

Mean count
2.2
Observed count
0
Exact-count probability
0.110803
Calculation method

Calculation method

Exact-count probability

exp(-a) × a^b ÷ (factorial(b))

Symbols and units
a
Mean count
b
Observed count

Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.

Calculation steps and notation

factorial(n) is 1 × 2 × … × n, with factorial(0) = 1. Exact integer arithmetic is used up to n = 500.

exp(x) means e^x, where e is approximately 2.718281828459045.

Assumptions & limits

Assumptions & limits

  • Poisson model with a constant mean event rate and independent events.
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Further reading

Method reference ↗

Background reading; this does not imply endorsement or independent review of SumFizz.

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