What formula does this use?

It uses Cochran's formula n = z² × p × (1 − p) / e², with an optional finite-population correction n / (1 + (n − 1) / N) when you supply a population size.

Why use 50% for the proportion?

A proportion of 50% maximises p × (1 − p), giving the largest and therefore safest required sample when you have no prior estimate.

Does a smaller population reduce the sample needed?

Yes. For small finite populations the correction lowers the required sample, since you are sampling a larger fraction of the whole.

Sample Size Calculator

How many responses you need for a survey.

Sample size calculator

This tool finds the survey sample size you need for a target margin of error and confidence level using Cochran’s formula n = z² · p(1−p) / e², with an optional finite-population correction when the total population is known.

Set your parameters and read the required number of respondents — all maths runs in your browser.