Confidence Interval for Proportion Calculator
When you survey a sample of people and count how many have a particular attribute, you get a sample proportion. But the true population proportion may differ from your sample result. A confidence interval gives a range of values that is likely to contain the true proportion. This calculator uses the Wald (normal approximation) method, which is widely used and works well when the sample size is large enough that both np and n(1-p) exceed 5. Enter the sample proportion as a percentage, the sample size, and your chosen confidence level to get the lower and upper bounds of the interval.
Confidence interval for proportion formula
CI = p ± z × √(p(1-p) / n)
Where p is the sample proportion (as a decimal), z is the critical value (1.645 for 90%, 1.960 for 95%, 2.576 for 99%), and n is the sample size. Results are expressed as percentages in this calculator.
When to use this interval
- Use this calculator when you have a binary outcome (yes/no, success/failure) and want to estimate the true population proportion.
- The Wald method works well when both np and n(1-p) are at least 5. For small samples or extreme proportions, consider the Wilson score interval.
- A 95% confidence interval is the most commonly used standard in social science, polling, and biomedical research.
- Poll results reported in the media typically use a 95% confidence level and describe the margin of error as plus or minus a percentage.
Frequently asked questions
What is a confidence interval for a proportion?
A confidence interval for a proportion estimates the range of plausible values for the true population proportion based on a sample. For example, if 60% of survey respondents agree with a statement, the 95% confidence interval tells you how much this estimate might vary from the true population percentage.
What formula does this calculator use?
It uses the Wald (normal approximation) formula: p plus or minus z times the square root of p(1-p)/n, where p is the sample proportion, z is the critical value, and n is the sample size. This approximation is reliable when both np and n(1-p) are at least 5.
When is the Wald interval not reliable?
The Wald interval can be inaccurate when p is close to 0 or 1, or when the sample size is small. In those cases, use the Wilson score interval or an exact (Clopper-Pearson) method for better coverage.
What critical z value is used for each confidence level?
For 90% confidence, z is 1.645. For 95% confidence, z is 1.960. For 99% confidence, z is 2.576. These are the values that cut off the appropriate tail areas of the standard normal distribution.
How do I enter the proportion?
Enter the proportion as a percentage. For example, if 60% of your sample has the characteristic of interest, enter 60. The calculator divides by 100 before applying the formula.
Official sources
- NIST/SEMATECH e-Handbook of Statistical Methods: Confidence Intervals for Proportions.
- NIST/SEMATECH e-Handbook: Engineering Statistics Handbook.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.