Confidence Interval Calculator

The Wilson score interval for a binomial proportion (Wilson, 1927). It is widely recommended as a default over the normal approximation (Wald) interval for survey percentages.

Inputs are successes x, sample size n, and a confidence level that sets z (about 1.645 / 1.960 / 2.576 for 90% / 95% / 99%).

With p̂ = x/n and critical value z:

center = (p̂ + z²/(2n)) / (1 + z²/n)

half-width = z × √(p̂(1−p̂)/n + z²/(4n²)) / (1 + z²/n)

Interval = center ± half-width, reported here as percentages.

Wald intervals center on the raw percentage and assume a large sample. They can produce nonsense bounds below 0% or above 100%, especially near extremes.

Wilson stays inside 0–100% and usually matches the stated confidence level more closely.

They are nominal confidence levels. A 95% interval is constructed so that, under the model assumptions, about 95% of such intervals from repeated samples would cover the true population percentage.

Higher confidence means a wider interval, not a “more accurate” point estimate.

NPS is a difference of two percentages, not a single binomial proportion. This tool is for one share (for example % promoters, % yes, or CSAT).

Calculate NPS with the NPS calculator, then use this page for individual category shares if you need intervals.

When you sampled without replacement from a known finite group (for example 80 of 200 employees) and that sample is a large fraction of the group.

Leave it blank for open web surveys or huge populations where the correction barely matters.

It reports the interval and an approximate half-width (half the distance between upper and lower bounds). That half-width is the practical “margin” around the Wilson center for communication, with the caveat that Wilson intervals are not perfectly symmetric around p̂.

No. Everything runs locally in your browser.

Use any survey tool, including Formms, then bring the success count and sample size here when you want a Wilson interval on the percentage.