Confidence Interval Calculator
Enter how many respondents fell into a group and your total, and get the interval the true proportion plausibly lies within.
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Observed 60.0% · 95% Wilson interval
This uses the Wilson score interval rather than the textbook Wald formula. Wald misbehaves near 0% and 100% and at small samples — it can even produce a bound below zero.
Why this uses Wilson, not Wald
Most calculators use the Wald interval: p ± z√(p(1−p)/n). It's the one in textbooks, and it breaks in exactly the cases people care about — small samples and results near 0% or 100%, where it can produce a lower bound below zero.
This uses the Wilson score interval, which is the standard recommendation and stays inside 0–100% by construction. At large samples with a mid-range result the two agree closely; at the edges Wilson is right and Wald isn't.
Questions people ask
What does a 95% confidence interval mean?
If you repeated the survey many times, about 95% of the intervals produced would contain the true value. It is not a 95% probability that the true value is in this particular interval, though that reading is common and mostly harmless in practice.
Why is my interval so wide?
Small sample. Interval width scales with 1/√n, so quadrupling your responses halves the width — there's no shortcut around collecting more.
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