Statistics

Binomial Distribution Calculator

The binomial distribution describes the number of successes in n independent trials, each with success probability p. Enter n, p and a target k to get the point probability P(X = k), the cumulative probabilities and the distribution's mean, variance and standard deviation.

Binomial Distribution Calculator

P(X = k), P(X ≤ k), P(X ≥ k) plus mean and variance for Binomial(n, p).

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Frequently asked questions

When is the binomial distribution appropriate?

When the trials are independent, each has exactly two outcomes (success / failure), and the success probability p stays constant across trials.

What is the mean of a binomial?

μ = n·p — the average number of successes you would expect across many repetitions of the n-trial experiment.

How is P(X ≤ k) computed?

By summing the point probabilities P(X = 0), P(X = 1), …, P(X = k). The calculator does this internally with log-arithmetic to stay accurate for large n.