Binomial confidence interval

Enter independent success/failure observations: sample size n and successes x. Results update as you type. The two-sided Wilson score interval uses the chosen normal critical value at 90%, 95% or 99% confidence, without a continuity correction. Input drafts, including unfinished values, remain in local browser storage through navigation and reload. Sample size must be between 1 and 1,000,000,000; successes must be whole numbers between 0 and n.

Confidence describes the long-run coverage of intervals constructed from repeated samples; it is not a probability assigned to this particular fixed population proportion. Wilson coverage is approximate, especially for small samples; this is not an exact Clopper–Pearson interval. Independent observations with a common success probability are assumed. Selection bias, correlation, changing populations and measurement error are not corrected.

Precision adapts to the interval width. Small positive percentages use scientific notation; values just below 100% are shown as 100% minus their positive complement. Exact observed 0% or 100% does not eliminate uncertainty: the Wilson interval retains a positive width. The line shows the interval and the dot shows the observed proportion. The axis zooms to the interval and labels the displayed range.