Proportion Confidence Interval Calculator
Calculate a Wilson score confidence interval for a binomial proportion, including zero or all observed successes.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Divide successes by the trial count. Choose the two-sided normal critical value. Calculate the Wilson center and half-width. Bound the resulting proportion interval between zero and one.
Center=(p+z²/(2n))/(1+z²/n); half=z√(p(1−p)/n+z²/(4n²))/(1+z²/n)
Worked example
With 50 successes in 100 trials, the 95% Wilson interval is approximately 40.383153% to 59.616847%.
Assumptions and input details
Whole counts, independent Bernoulli trials and one fixed success probability are assumed. This is a Wilson interval, not an exact Clopper-Pearson interval, a prediction interval or a correction for biased sampling.
References: NIST: confidence intervals for a proportion
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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