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THE FEUTEX TOOLKIT

Wilson Proportion Interval

Calculate a Wilson score confidence interval for a proportion from successes and trials.

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01 Your input
02 Your result
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FormulaProportion = k/n; Lower = ((k/n)+z**2/(2*n))/(1+z**2/n)-(z*sqrt((k/n)*(1-(k/n))/n+z**2/(4*n**2))/(1+z**2/n)); Upper = ((k/n)+z**2/(2*n))/(1+z**2/n)+(z*sqrt((k/n)*(1-(k/n))/n+z**2/(4*n**2))/(1+z**2/n))
Sources and model references

Worked example

Inputs

Successes
50 count
Trials
100 count
Normal critical value
1.96 number

Expected results

Proportion
0.5 number
Lower
0.4038298286 number
Upper
0.5961701714 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter the labeled inputs using consistent units.
  2. Check the stated assumptions and calculate.
  3. Review each output and compare another input scenario.

Try this example

{
  "k": 50,
  "n": 100,
  "z": 1.96
}

Accuracy and scope

Independent Bernoulli observations; z=1.96 corresponds approximately to 95% confidence. Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.