Binomial Confidence Interval Calculator

This calculator finds a confidence interval for a binomial proportion using the Wilson score method, a more accurate approach than the simple textbook formula, especially for small samples and proportions near zero or one. When you observe a number of successes out of a number of trials, the proportion you measure is only an estimate of the true underlying rate, and a confidence interval expresses the uncertainty. The familiar Wald interval, the proportion plus or minus a margin, is simple but performs poorly when the sample is small or the proportion is extreme, sometimes even producing bounds below zero or above one. The Wilson score interval fixes these problems: it stays within the valid zero-to-one range, has better coverage, and is the method statisticians recommend for proportions. This calculator computes it. You enter the number of successes, the number of trials, and the confidence level, and it returns the Wilson confidence interval, the observed proportion, and the lower and upper bounds. The results update as you type. Use it to report a proportion with honest uncertainty, for A/B testing and conversion rates, for survey results, or for quality and reliability data. The Wilson interval centres not on the raw proportion but on a slightly adjusted value, and its width accounts for both the sampling variability and the sample size in a way that behaves well at the extremes. Because of this it is particularly valuable when you have few trials or a proportion close to a boundary, exactly the situations where the simpler interval misleads. A wider confidence level, such as 99 percent, gives a wider interval. This complements the Wald-style interval some tools provide: where the Wald interval is a quick approximation, the Wilson score interval is the more trustworthy choice, and it is what you should prefer when accuracy matters.

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Wilson score interval: stays within 0-100% and is accurate for small samples and extreme proportions, unlike the simple Wald interval. Choose the confidence level.