Binomial Distribution Calculator
Work out exact and cumulative binomial probabilities — enter the number of trials, the chance of success and how many successes you want, and see every step.
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Use nowHow the Binomial Distribution Calculator Works
A binomial distribution answers questions like "if I toss a coin 10 times, what is the chance of exactly 5 heads?" You need three numbers: n, the number of trials; p, the probability of success on a single trial; and k, the number of successes you are asking about. The calculator works out P(X = k) with the binomial formula P(X = k) = C(n, k) × pk × (1 - p)n-k, and shows the combinations count and the substituted numbers so you can follow the working.
It also gives the cumulative probabilities — P(X ≤ k), P(X ≥ k), P(X < k) and P(X > k) — plus the mean n × p, the variance n × p × (1 - p) and the standard deviation. Below the answers there is a probability table for every value of k from 0 to n (for large n it shows the key rows instead). Try the example: n = 10, p = 0.5, k = 5 gives P(X = 5) = 0.246094, about a 24.61% chance, with a mean of 5.