# 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.

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