Exact binomial test calculator
Test a success probability without using the normal approximation.
How to use this page
- Enter successes and trials.
- Provide p₀ and the pre-specified test direction.
- Read the p-value together with p̂ and both tails.
What this page does not do: Trials must be independent with constant success probability. The test does not measure practical effect size and does not replace a confidence interval.
Further reading
The exact binomial test compares an observed success count with Bin(n,p₀). A one-sided test sums the chosen tail. The two-sided version sums outcomes no more probable under H₀ than the observed result.
A p-value is not the probability that H₀ is true. It measures compatibility of the data with the model after assuming H₀.
Frequently asked questions
Why is the two-sided p-value not always twice the one-sided value?
The binomial distribution is discrete, so the exact test sums outcomes by their probabilities and is not always symmetric.
Can x be 0 or n?
Yes. The exact distribution includes both boundary outcomes.
See also
Beta distribution calculator
Calculate beta density, CDF, upper tail and quantile together with its mean and variance.
Chi-square test calculator
Calculate chi-square goodness of fit, independence, or a chi-square critical value.
Continuous uniform distribution calculator
Calculate density, CDF, upper tail, quantile, mean and variance for U(a,b).