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.
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.