Sample Size Calculator (Margin of Error)

The minimum sample size needed to estimate a population proportion within a target margin of error e, at a target confidence level, is n = z² × p(1−p) ÷ e², where z is the critical value of the standard normal distribution for that confidence level (computed from an inverse-normal-CDF approximation, not a fixed lookup table, so any confidence level works, not just the usual 90/95/99%) and p is the proportion you expect to find.

p defaults to 50% because p(1−p) is largest there — if you genuinely have no idea what proportion you're measuring, 50% is the most conservative assumption and gives the largest (safest) required sample size. If you have a reasonable prior estimate (say, from a pilot study), entering it instead will usually lower the required sample size.

When the population you're sampling from is of a known, finite size, the infinite-population estimate above is reduced with the standard finite population correction, n' = n ÷ (1 + (n−1)/N) — leaving the population size at 0 skips this and treats the population as large enough that it doesn't matter.