Binomial probability calculator
Find the probability of a number of successes in n independent trials with constant success probability p.
Probabilities around k
| Successes k | P(X = k) |
|---|---|
| Fill in the fields above — the result is computed on this page. | |
How do I use this page?
- Choose exact, at most or at least.
- Enter n, p and k.
- Compare the point probability with the two tails.
What this page does not do: The model does not fit dependent trials or trials whose success probability changes.
Further reading
Theory — what is the binomial distribution?
The binomial distribution describes the number of successes in a fixed number n of independent trials, each with the same success probability p. A typical example is flipping a coin dozens of times or sampling with replacement from a large population. The calculator returns the exact probability for a given count of successes as well as both tails of the distribution. Probability p is entered as a value between 0 and 1, such as 0.2 instead of 20%.
Frequently asked questions
Should p be entered as a percentage?
How is this different from a binomial test?
See also
A/B test calculator
Compare two proportions in an A/B test. Calculate conversion rates, difference, uplift, z score, p value and c
A/B test planning — sample size, MDE and duration
Plan a two-proportion experiment, estimate detectable effect and traffic duration.
ACF and PACF autocorrelation calculator
Calculate ACF and PACF across time-series lags. Review the chart, reference bounds and coefficient table.