Confidence Interval for a Proportion Calculator
Estimate a proportion and its Wilson score interval from a count of successes and a total sample size.
How to use this calculator
- Enter integer successes, total observations and the confidence z-score, such as 1.96 for approximately 95%.
- Check that every input uses the stated units and covers the same period, population or project scope.
- Change one assumption at a time when comparing scenarios.
Formula used by confidence interval proportion calculator
Wilson interval using observed p, sample size n and confidence z-score
- Wilson interval using observed p, sample size n and confidence z-score
- The interval assumes observations can reasonably be treated as independent; survey design and selection bias are not corrected.
- Inputs are validated against the tool-specific constraints; displayed results are rounded for readability.
Worked examples
Worked example
If 54 out of 100 observations meet a condition, the observed proportion is 54%; the interval also reflects sampling uncertainty.
The Wilson score method calculates lower and upper bounds for the entered z-score.
The Wilson score method calculates lower and upper bounds for the entered z-score.
Understanding the result
Estimate a proportion and its Wilson score interval from a count of successes and a total sample size.
The interval assumes observations can reasonably be treated as independent; survey design and selection bias are not corrected.
Important notes
The interval assumes observations can reasonably be treated as independent; survey design and selection bias are not corrected.
Treat the result as an estimate for the assumptions entered; verify important specifications against the relevant source or professional guidance.
Frequently asked questions
Why use a Wilson interval?
It generally behaves better than the simple Wald interval for small samples and proportions near zero or one.
Does the interval remove sampling bias?
No. It quantifies sampling uncertainty under assumptions and does not correct biased sampling or measurement.
How should I use this result?
Enter integer successes, total observations and the confidence z-score, such as 1.96 for approximately 95%.
Related calculators
- Confidence Interval for Mean Calculator — Estimate a normal-approximation confidence interval around a sample mean from its spread and sample size.
- Sample Size for a Proportion Calculator — Estimate sample size for a proportion at a chosen confidence z-score and margin of error.
- Sample Size for a Mean Calculator — Estimate the sample size needed to estimate a population mean for a stated standard deviation, margin of error and confidence z-score.
- Sample Size Calculator — Estimate a simple random-sample size for a proportion using a chosen confidence z-score, assumed proportion and margin of error.
- Proportion Calculator — Solve a simple proportion with three known values.
- Two-Proportion Z-Test Calculator — Compare two independent success proportions using a pooled z statistic and a two-sided normal approximation.
Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate Days Between Dates — Learn how date intervals work, including leap years and inclusive vs exclusive day counting.
- How to Calculate a Z-Score — Learn how a z-score shows how far a value is from the mean in standard-deviation units.
- Percent Difference — Understand percent difference, when it is appropriate, and how it differs from percentage change and percent error.
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.