Wilson Interval Center
Use this wilson interval center tool when you have measured values for successes, trials, z. It applies a transparent mathematical relationship to those values to return an answer in ratio. Unlike a prediction or recommendation, this is a calculation from your inputs. Wilson center is only one part of the confidence interval. Enter a different scenario to see how this particular quantity changes; check the assumptions before using it in a project.
How to use this calculator
- Use exact measurements and consistent units for successes, trials, z.
- Enter each quantity; blank, nonnumeric and out-of-range inputs are not accepted.
- Compare the reported ratio quantity against your own data and the limitations below.
Formula for Wilson Interval Center
ratio = (successes+z*z/2)/(trials+z*z). Inputs are expressed in the units shown by the labels.
- This uses a direct stats relationship and does not retrieve remote data, forecasts or individual account information.
- Wilson center is only one part of the confidence interval.
Worked examples
Worked example — Wilson Interval Center
Enter Successes = 45, Trials = 100, Z = 1.96.
Apply (successes+z*z/2)/(trials+z*z).
Calculated value: approximately 0.4518497 ratio.
Understanding the result
The example produces about 0.4518497 ratio; this is a mathematical output for the example inputs, not an observed result for your project.
Wilson center is only one part of the confidence interval.
Important notes
Wilson center is only one part of the confidence interval.
Use values from the same measurement period or physical system. The result is in ratio and is not a guarantee of capacity, safety, ranking or revenue.
Frequently asked questions
What does Wilson Interval Center calculate?
It converts successes, trials, z into a quantity measured in ratio using the stated formula.
Which assumption matters most?
Wilson center is only one part of the confidence interval.
How can I check this output?
Recalculate the worked example from the input quantities, confirm units and compare with direct measurements where available. This calculator does not fetch live data.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.