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Wilson Proportion Interval Calculator

Wilson interval uses center (p+z²/(2n))/(1+z²/n) and its score half-width.

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  1. 01

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Calculate Wilson proportion interval online

Wilson interval uses center (p+z²/(2n))/(1+z²/n) and its score half-width. Use this to calculate a stated mathematical relationship from your own explicit assumptions. Units and input order are part of the calculation; no changing external rates or laws are inferred.

How to use it

Enter 3 comma-separated numbers in this order: successes, trials, critical z multiplier. Choose Calculate. Review the output, then copy or download it.

Calculation method

Wilson interval uses center (p+z²/(2n))/(1+z²/n) and its score half-width.

Worked examples

Use this to calculate a stated mathematical relationship from your own explicit assumptions. Units and input order are part of the calculation; no changing external rates or laws are inferred.

Reproducible worked example

Settings: No additional settings.

Input:

45, 100, 1.96

With the input and settings above, the tool produces:

Output:

{
  "observedProportion": 0.45,
  "lower": 0.3561437510640346,
  "upper": 0.5475557296835656
}

For this input, “observedProportion” is 0.45; “lower” is 0.3561437510640346; “upper” is 0.5475557296835656. These are the named fields in the example output.

Limitations and common mistakes

  • Supply the appropriate critical multiplier. Binomial sampling assumptions and study design are not verified.
  • Combined input is bounded to 150,000 characters; output text is bounded to 1.2 million characters. Some algorithms impose smaller limits, stated in their error messages.
  • Use a dot as the decimal separator and commas or spaces between numeric entries. The calculation uses floating-point arithmetic unless exact integers are explicitly stated.

Frequently asked questions

What format should I enter?

Enter 3 comma-separated numbers in this order: successes, trials, critical z multiplier. The worked example shows the supported structure and actual output.

How can I compute Wilson proportion interval online?

Enter 3 comma-separated numbers in this order: successes, trials, critical z multiplier. Choose Calculate. Review the output, then copy or download it.

Where is my input processed?

The bundled tool processes input in your browser. It does not upload tool input to a conversion service. Other site plugins, analytics, advertising and browser extensions may have separate behavior.

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