Confidence Interval for a Proportion Calculator
Confidence interval around a sample proportion.
Enter your values
ⓘ Live results
Results
- Confidence interval
- 0.341 to 0.499
- Margin of error
- ±0.079
- Standard error
- 0.0403
Quick answer
The confidence interval for a proportion is p̂ ± z*sqrt(p̂(1-p̂)/n), using the z critical value for the chosen confidence level.
CI = p̂ ± z*sqrt(p̂(1-p̂)/n)
How to use the Confidence Interval for a Proportion Calculator
- 1Enter your sample proportion (successes divided by sample size).
- 2Enter the sample size and desired confidence level.
- 3The margin of error uses the z critical value times the standard error.
Worked example
Using the values the calculator loads with:
Inputs
- Sample proportion0.42
- Sample size150
- Confidence level95%
Results
- Confidence interval0.341 to 0.499
- Margin of error±0.079
- Standard error0.0403
Frequently asked questions
Which confidence level should I use?
95% is the most common default in research and reporting.
What if n is small?
For small samples, consider an exact binomial confidence interval instead of this normal approximation.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.