Binomial Distribution Calculator
Calculate binomial probabilities: exactly k, at most k, at least k.
All calculations happen locally in your browser — nothing is uploaded, stored or tracked.
Enter trials (n)
The number of independent trials.
Enter success probability (p)
As a percentage.
Enter k
The number of successes you are interested in.
What Is the Binomial Distribution?
The binomial distribution models the number of successes in a fixed number of independent trials, where each trial has the same success probability — flipping a coin 10 times and counting heads, or checking 50 products for defects.
The calculator finds the probability of exactly k successes, the cumulative probability of at most k, and at least k, plus the distribution's mean, variance and standard deviation.
The Formula
For large numbers of trials the binomial coefficient is computed in log space to avoid overflow, so values up to n = 5,000 are handled without errors.
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Frequently Asked Questions
What is a binomial distribution?
It models the number of successes in n independent trials with a constant success probability, such as coin flips or pass/fail checks.
How do I calculate binomial probability?
Use C(n,k) × pᵏ × (1−p)^(n−k). For example, exactly 3 heads in 5 coin flips: C(5,3) × 0.5³ × 0.5² = 31.25%.
What is C(n, k)?
The binomial coefficient — the number of ways to choose k items from n. Also written "n choose k".
When can I use the binomial distribution?
When trials are independent, the number is fixed, and each trial has the same two outcomes (success/failure).
What are the mean and variance?
Mean = np, variance = np(1−p). The calculator shows both.