Confidence Interval for a Proportion (Wilson)
Wilson-score confidence interval for a binomial proportion (events ÷ n) at a 90/95/99% level — the small-sample-honest interval for a rate.
Open the calculator → Runs in your browser. Data leaves only if you deliberately send a problem report from the interactive tool.
Example
- Number of events
- 8
- Sample size n
- 10
- Confidence level
- 95%
Result: Proportion 80% (95% CI 49–94.3%).
The tool opens with these values already filled in. Replace them with your own.
What the result means
- Use
- Stays within [0, 1] and behaves well for small n or proportions near 0/1, unlike the naive Wald interval.
What you enter
- Number of events
- Sample size n
- Confidence level
How this is calculated
- Formula
- Center = (p̂ + z²/2n)/(1 + z²/n); half = (z/(1 + z²/n))·√(p̂(1−p̂)/n + z²/4n²); clamped to [0, 1].
Wilson EB. Probable inference, the law of succession, and statistical inference. J Am Stat Assoc. 1927;22(158):209-212. Read the source ↗
A reference and educational tool. Not medical, legal, or financial advice, and not a substitute for clinician judgment.