Confidence Interval Calculator
Calculate Wilson, exact, Wald, and mean confidence intervals with the method and assumptions shown.
At a glance
- Computes
- Wilson, Clopper-Pearson, and Wald proportion intervals, plus a t interval for a mean.
- You supply
- Successes and trials, or a sample mean, SD, and size, plus a confidence level.
- Use when
- You need the range one estimate is consistent with, at a stated confidence level.
- Not for
- The interval around a difference between two groups. A/B Test Calculator
95 percent confidence interval (proportion)
Confidence interval
Enter values
Wilson is the default for proportions.
| Metric | Value |
|---|
Wilson: (p + z^2/(2n)) / (1 + z^2/n), with Wilson half-width
How?
How this is calculated
Proportion intervals default to Wilson score because it behaves better near 0 and 1 than the plain Wald interval. Clopper-Pearson exact is available for binomial boundary cases, and mean intervals use the one-sample t interval with sample SD.
Formula: Wilson: (p + z^2/(2n)) / (1 + z^2/n), with Wilson half-width
Formula intervals and resampling intervals answer neighboring questions
Every interval on this page rests on a distributional assumption, which is what makes it a formula rather than a simulation. The bootstrap instrument resamples one sample you already have and reads an interval off that distribution. The central limit theorem instrument draws from a known population and shows why a sampling distribution has the shape these formulas assume.
Combining several intervals is a different procedure
Each interval above is computed from a single sample. Combining several intervals that estimate the same quantity is a separate procedure: every estimate enters with a weight set by its own precision, and the variation between them has to be estimated as well. The meta-analysis instrument runs that procedure and reports the pooled estimate with its interval.
Sources
- statsmodels proportion_confint. statsmodels. Retrieved .
- NIST SEMATECH e-Handbook confidence intervals. NIST. Retrieved .
Method last reviewed