Sample Size Calculator

Use n = z² × p(1 − p) ÷ e², where z is the critical value for your confidence level, p is the expected proportion (use 0.5 for the most conservative, largest sample), and e is your margin of error as a decimal. Always round the result up, since you cannot survey a fraction of a person.

The term p(1 − p) is largest when p = 0.5, which produces the maximum required sample size. Using 50% is the safe, conservative choice when you have no prior estimate of the proportion — it guarantees your sample is big enough no matter what the true value turns out to be.

When your total population is small, you do not need as large a sample. The correction n = n₀ ÷ (1 + (n₀ − 1)/N) reduces the required size based on the population N. For very large or unknown populations, the correction has almost no effect, so you can leave the population field blank.

Sample size grows with the square of the inverse of the margin of error. Halving the margin of error (say from 5% to 2.5%) quadruples the required sample. That is why very precise surveys need dramatically more respondents than rough ones.

A higher confidence level uses a larger z-value, which increases the required sample size. Going from 95% (z = 1.96) to 99% (z = 2.576) roughly increases the needed sample by about 73%, because the z-value is squared in the formula.