# Poisson Distribution Calculator

 Enter Number of Occurrences (n) Enter probability of success (p) Enter Number of successes (k) Enter Moment Number t (Optional)

Using a Poisson distribution with a probability of success of 0.4, calculate the Probability of having exactly 0 successes in 10 tries. Start with the Poisson Distribution formula below:
 P(k; λ)  = λk eλk!

Calculate λ
λ = p * n
λ = 0.4 * 10
λ = 4

Calculate k!:
k! = 0!
0! =
0! = 1

Calculate the probability:
 P(k; λ)  = λk eλk!

 P(0; 4)  = 40 2.7182818284(0!)

 P(0; 4)  = 1 54.598150033144 * 1

 P(0; 4)  = 1 54.5982

## Excel or Google Sheets formula:

=POISSON(0,4,FALSE)

P(0; 4) = 0.0183

### How does the Poisson Distribution Calculator work?

Free Poisson Distribution Calculator - Calculates the probability of 3 separate events that follow a poisson distribution.
It calculates the probability of exactly k successes P(x = k)
No more than k successes P (x <= k)
Greater than k successes P(x >= k)
Each scenario also calculates the mean, variance, standard deviation, skewness, and kurtosis.
Calculates moment number t using the moment generating function
This calculator has 4 inputs.

### What 2 formulas are used for the Poisson Distribution Calculator?

1. λ p * n
2. P(k; λ) = λk/eλk!

For more math formulas, check out our Formula Dossier

### What 9 concepts are covered in the Poisson Distribution Calculator?

distribution
value range for a variable
event
a set of outcomes of an experiment to which a probability is assigned.
factorial
The product of an integer and all the integers below it
mean
A statistical measurement also known as the average
moment
a function are quantitative measures related to the shape of the functions graph
poisson distribution
a discrete probability distribution that is used to show how many times an event is likely to occur over a specified period.
probability
the likelihood of an event happening. This value is always between 0 and 1.
P(Event Happening) = Number of Ways the Even Can Happen / Total Number of Outcomes
standard deviation
a measure of the amount of variation or dispersion of a set of values. The square root of variance
variance
How far a set of random numbers are spead out from the mean

## Tags:

Calculate the mean μ and variance σ2:
In the poisson distribution, mean and variance = λ
μ = λ
μ = 4

σ2 = λ
σ2 = 4

Calculate the standard deviation σ:
σ = √σ2
σ = √4
σ = 2

## Calculate Skewness:

 Skewness  = 1 √λ

 Skewness  = 1 √4

 Skewness  = 1 2

Skewness = 0.5

## Calculate Kurtosis:

 Kurtosis  = 1 λ

 Kurtosis  = 1 4

Kurtosis = 0.25