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Binomial Distribution Calculator
Enter the number of trials, the probability of success on each trial, and a target number of successes to calculate the binomial probability.
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What is the Binomial Distribution?
The binomial distribution describes the number of successes in a fixed number of independent trials, each with the same probability of success — think of quality control sampling, survey responses, or repeated experiments.
The Formula
P(X=k) = C(n,k) × p^k × (1−p)^(n−k), where n is the number of trials, p is the probability of success on each trial, and k is the number of successes. The mean of the distribution is n×p and its variance is n×p×(1−p).
- Choose “exactly,” “at least,” or “at most” to match the question you’re answering.
- Probability of success should reflect a single, independent trial.
Provided for general statistical education and planning purposes.
Last reviewed August 2026