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Wilson-Score Confidence Interval for a Proportion Calculator

Better than Wald CI when p is near 0 or 1 or n is small.

Compute the Wilson-score confidence interval for a binomial proportion p̂ = x/n. Unlike the standard Wald CI, the Wilson interval has good coverage even at small n or extreme p. Center = (p̂ + z²/(2n)) / (1 + z²/n); margin = z · √(p̂(1−p̂)/n + z²/(4n²)) / (1 + z²/n).

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

(p̂ + z²/(2n)) / (1 + z²/n) ± z · √(p̂(1−p̂)/n + z²/(4n²)) / (1 + z²/n).

In depth

Compute the Wilson-score confidence interval for a binomial proportion p̂ = x/n. Unlike the standard Wald CI, the Wilson interval has good coverage even at small n or extreme p. Center = (p̂ + z²/(2n)) / (1 + z²/n); margin = z · √(p̂(1−p̂)/n + z²/(4n²)) / (1 + z²/n).