Confidence Interval for Proportion Calculator


Instructions: Use this step-by-step Confidence Interval for Proportion Calculator, by providing the sample data in the form below:

Number of favorable cases \((X)\) =
Sample Size \((N)\)
Sample Proportion (Provide instead of \(X\) if known)
Confidence Level (Ex: 0.95, 95, 99, 99%) =



Confidence Interval for a Population Proportion

A confidence interval is a statistical concept that has to do with an interval that is used for estimation purposes. A confidence interval has the property that we are confident, at a certain level of confidence, that the corresponding population parameter, in this case the population proportion, is contained by it. For the case the population proportion (\(p\)), the following expression for the confidence interval is used:

\[ CI(\text{Proportion}) = \displaystyle \left(\hat p - z_c \sqrt{\frac{\hat p (1-\hat p)}{n}}, \hat p + z_c \sqrt{\frac{\hat p (1-\hat p)}{n}}\right) \]

where the critical value correspond to critical values associated to the Normal distribution. The critical values for the given \(\alpha\) is \(z_c = z_{1 - \alpha/2}\).

The basis for this confidence interval is that the sampling distribution of sample proportions (under certain general conditions) follows an approximate normal distribution.

Assumptions that need to be met

It is crucial to check for the assumptions required for constructing this confidence interval for population proportion. In this case we need the normality assumption, which is required because ultimately we have a binomial variable involved, so certain assumptions are needed. Typically, we require that \(n \hat p \ge 10\) and \(n (1-\hat p) \ge 10\).

Observe that if you want to use this calculator, you already need to have summarized the total number of favorable cases \(X\) (or instead provide the sample proportion). This is not a confidence interval calculator for raw data. If you have raw data, you need to summarize it first.

Notice that this calculator works for estimating the confidence interval for one population proportion. When you are dealing with two population proportions, what you want is to compute a confidence interval for the difference between two population proportions.

Other Calculators you can use

You are probably interested in calculating other confidence intervals. For example, you can use our confidence interval for the mean, or this confidence interval for variance when mean is known, or you can also this confidence interval for mean regression responses, as well as our calculator for a confidence interval for the variance.




In case you have any suggestion, or if you would like to report a broken solver/calculator, please do not hesitate to contact us.

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