Confidence Interval for a Proportion Calculator
Puts a range around a percentage from a sample.
Wilson interval
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Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.
Wald interval —
Observed proportion — %
Reading this —
The formula
Wald: p ± z√(p(1 − p) ÷ n) Wilson: (p + z²/2n ± z√(p(1 − p)/n + z²/4n²)) ÷ (1 + z²/n)
The Wilson interval is the one left after solving the test of a proportion for its boundary values. It stays within 0% to 100%.
What to watch out for
For a sample with no successes, the Wald interval collapses to nothing, which is plainly wrong. The Wilson interval still gives a sensible upper bound.
Frequently Asked Questions
What is the interval for 0 successes in 20?
The Wilson 95% interval runs from 0% to 16.1%, while the Wald interval is just 0%.
How is it different from the margin of error page?
That page uses the Wald formula. It suits a large survey, and this page is safer for smaller samples.