Poisson Distribution Calculator
Find Poisson probabilities for a number of events given an average rate: exactly, fewer than, at most, more than and at least x.
Change the values and press Calculate to work out your own figures.
Enter the number of events and the average rate.
Show the working
- P(X = x) = λ^x × e^(−λ) ÷ x!
- = 2^3 × e^(−2) ÷ 3! = 0.1804470443
How to use it
Enter the number of events and the average rate.
Probabilities can be typed as decimals, fractions or percentages. Show the working gives the formula with your numbers in it.
Key facts
P(X = x) = λˣ e^(−λ) ÷ x!
Counting rare events
The Poisson distribution models how many times something happens in a fixed interval when events are independent and happen at a steady average rate, such as calls to a help line per hour.
Questions
What is λ?
The average number of events per interval; it is also the variance.
Can λ be a decimal?
Yes; x must be a whole number.
Formulas
P(X = x) = λˣ e^(−λ) ÷ x!
Sources
Limitations
- Probabilities can be typed as decimals (0.25), fractions (1/4) or percentages (25%).