Wilson score interval calculator
Enter the number of successes and total sample size. The Wilson method is more stable than the simple Wald interval for small samples and proportions near 0 or 1.
How do I use this page?
- Enter successes and n.
- Choose the confidence level.
- Read the lower and upper bounds.
What this page does not do: The model assumes independent Bernoulli observations with a constant success probability.
Further reading
Theory — what is the Wilson score interval?
The Wilson score interval estimates a confidence interval for a proportion from the number of successes and the total sample size. Unlike the simple Wald interval, it is not just the proportion plus or minus an error margin — it adjusts the centre and width using the term z²/n, so the bounds always stay within 0 and 1. This makes it more stable than Wald for small samples. A confidence level such as 95% describes the long-run coverage of the procedure across repeated samples, not certainty about a single result.
Frequently asked questions
Why is the center different from p̂?
Can the result go below 0 or above 1?
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.