Wilson Score Interval Calculator
Use this interval when you need a more stable confidence range for a proportion than a simple normal approximation, particularly when the sample is modest or the observed rate is near zero or one.
How to use this calculator
- Enter the observed successes using the units shown beside the field.
- Enter the total trials using the units shown beside the field.
- Enter the z multiplier (e.g. 1.96 for about 95%) using the units shown beside the field.
- Review the calculated values and check that the assumptions match your scenario.
- Change one input at a time when comparing scenarios so you can see which assumption drives the result.
Formula and assumptions
Wilson interval for proportion p: center=(p+z²/(2n))/(1+z²/n); half-width=z·sqrt(p(1-p)/n+z²/(4n²))/(1+z²/n).
- The z multiplier determines the confidence level approximately; 1.96 is commonly used for a two-sided 95% interval. This is a statistical estimate, not a guarantee about future outcomes.
- The result is computed from the values you provide; it does not fetch external rates, live account data or local rules.
Worked examples
Worked example
With 42 successes out of 60 and z=1.96, the point estimate is 70%; the Wilson interval is approximately 57.5% to 80.1%.
Example inputs: Observed successes = 42, Total trials = 60, Z multiplier (e.g. 1.96 for about 95%) = 1.96.
Compare the displayed output with your own measurements before using it in a decision.
Understanding the result
The z multiplier determines the confidence level approximately; 1.96 is commonly used for a two-sided 95% interval. This is a statistical estimate, not a guarantee about future outcomes.
Results are estimates based on the stated model. If the situation depends on measured conditions or contractual specifications, use those source values rather than typical assumptions.
Important notes
The z multiplier determines the confidence level approximately; 1.96 is commonly used for a two-sided 95% interval. This is a statistical estimate, not a guarantee about future outcomes.
Frequently asked questions
What formula does this calculator use?
It uses the method described above: Wilson interval for proportion p: center=(p+z²/(2n))/(1+z²/n); half-width=z·sqrt(p(1-p)/n+z²/(4n²))/(1+z²/n).
What should I verify before relying on the result?
The z multiplier determines the confidence level approximately; 1.96 is commonly used for a two-sided 95% interval. This is a statistical estimate, not a guarantee about future outcomes.
Can I compare different scenarios?
Yes. Change the inputs while keeping units and definitions consistent, and record the assumptions used for each scenario.
Related calculators
- Confidence Interval for a Proportion Calculator — Calculate a Wilson score confidence interval for a proportion from observed successes and total observations.
- Confidence Interval for Mean Calculator — Estimate a normal-approximation confidence interval around a sample mean from its spread and sample size.
- One-Proportion Z-Test Calculator — Compare an observed sample proportion with a user-specified null proportion using a normal-approximation z test.
- Proportion Calculator — Solve a simple proportion with three known values.
- Z-Score Calculator — Calculate the z-score of a value using its mean and standard deviation.
- Binomial Probability Calculator — Calculate the probability of exactly a chosen number of successes in independent trials with the same success probability.
Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate a Z-Score — Learn how a z-score shows how far a value is from the mean in standard-deviation units.
- How to Calculate Days Between Dates — Learn how date intervals work, including leap years and inclusive vs exclusive day counting.
- Z-Score — Learn what a z-score measures and how it describes a value relative to a mean and standard deviation.
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.