Find the probability of a given number of successes in a fixed number of independent trials. Enter the number of trials, the number of successes you care about, and the probability of success on each trial, and the tool returns the exact probability plus the cumulative probability of at most and at least that many successes. The exact value uses the binomial formula, the combination of n choose k times p to the k times one minus p to the remaining trials. This models coin flips, quality inspections, free throw streaks, and any yes or no experiment repeated under the same odds. The tool also reports the expected number of successes and the standard deviation of the distribution. Combinations are computed with a stable multiplicative loop to avoid overflow. Everything runs locally in your browser, so your inputs stay on your device.
It applies to a fixed number of independent trials, each with the same success probability, such as coin flips.
Exact is the chance of precisely k successes, at most sums up to k, and at least sums from k upward.
It needs the number of trials, the number of successes and the probability of success on each trial.
Find the probability of a given number of successes in a fixed number of independent trials. Enter the number of trials, the number of successes you care about, and the probability of success on each trial, and the tool returns the exact probability plus the cumulative probability of at most and at least that many successes.
Yes. Binomial Probability Calculator is completely free, with no sign-up and no usage limits.
Yes. Binomial Probability Calculator runs in any modern web browser. There is nothing to download or install.
Yes. Binomial Probability Calculator runs entirely on your device in your browser, so nothing you enter is uploaded to a server.