Binomial Distribution Calculator

Binomial probabilities P(X = k), P(X ≤ k) and P(X ≥ k) with mean, variance and the full probability chart.

Your result will appear here

Fill in the fields and press Calculate, or pick one of the examples.

About the Binomial Distribution Calculator

The binomial distribution counts successes in n independent trials that each succeed with probability p. This calculator gives the probability of exactly k successes, at most k and at least k, with the mean and variance and a chart of the whole distribution.

Limitations

n up to 1,000,000. The chart shows the range within about five standard deviations of the mean.

How to use it

Enter the number of trials n and the success probability p.
Enter the number of successes k.
Press Calculate.

Example

n = 10, p = 0.5, k = 3

→ P(X = 3) = 0.1171875

Formulas used

P(X = k) = \binom{n}{k} p^{k} (1 - p)^{n - k}

Probability mass function.

\mu = np,\qquad \sigma^{2} = np(1 - p)

Mean and variance.

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About the Binomial Distribution Calculator

Limitations

How to use it

Formulas used

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About the Binomial Distribution Calculator

Limitations

How to use it

Formulas used