Minimum Sample Size Required Calculator – Estimating a Population Proportion

Instructions: This calculator finds the minimum sample size required to estimate a population proportion (\(p\)) within a specified margin of error. Please select type the the significance level (\(\alpha\)) and the required margin of error (E), along with an estimate of the population proportion if one exists, and the solver will find the minimum sample size required:

Required Margin of Error (E)
Estimate of pop. proportion (leave empty if none)
Significance level (\(\alpha\))

Minimum Required Sample Size for a Set Maximum Error

More information about the minimum sample size required so you can better use the results delivered by this solver: In general terms, the larger the sample size n, the more precise of an estimate can be obtained of a population parameter, via the use of confidence interval. In this case specifically, use the formula for the margin of error of a confidence interval for a population proportion \(p\):

\[E = z_c \sqrt{\frac{\hat p(1-\hat p)}{n} } \]

So, it can be observed from the above formula that if the sample size n increases (which is in the denominator), the margin of error \(E\) will decrease, provided that that the critical value \(z_c\) and \(\hat p\) do not change. So, the formula for obtaining the required sample size is obtained by taking the above equation and solving for n.

If you want to find instead a confidence interval for the mean, please use this confidence interval calculator .

This sample size calculator is for the population proportion. If you are dealing with a population mean instead of a population proportion, you should use our minimum required sample size calculator for population mean .

log in to your account

Don't have a membership account?

reset password

Back to
log in

sign up

Back to
log in