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    Binomial Probability Calculator Tool

Instructions: Compute binomial probabilities using the form below. Please type the population proportion of success p, and the sample size n, and provide details about the event you want to compute the probability for (notice that the numbers that define the events need to be integer):

Population proportion (p)
Sample Size (n)
Two-Tailed:    ≤ X ≤
Left-Tailed:    X ≤
Right-Tailed:    X ≥



More about the binomial distribution probability so you can better use this binomial calculator: The binomial probability is a type of discrete probability distribution that can take random values on the range of \([0, n]\), where \(n\) is the sample size. The main properties of the binomial distribution are:

  • It is discrete, and it can take values from 0 to n, where n is the sample size

  • The type of skewness depends on the parameters n and p

  • It is determined by two parameters: the population proportion of success, the sample size (or number of trials)

  • Its mean is \(n\cdot p\) and its standard deviation is \(\sqrt{np(1-p)}\)

Using the above binomial distribution curve calculator, we are able to compute probabilities of the form \(Pr(a \le X \le b)\), of the form \(\Pr(X \le b)\) or of the form \(\Pr(X \ge a)\). Type the appropriare parameters for \(n\) and \(p\) in the text box above, select the type of tails, specify your event and compute your binomial probability.

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