Work backward from the margin of error you want to the number of responses that gets you there.
The result panel updates the instant any field on the left changes.
With the defaults above (95% confidence, a 5% margin, an unknown 50% proportion, infinite population): n0 = 1.96 squared times 0.5 times 0.5, divided by 0.05 squared. That is 0.9604 divided by 0.0025, which comes out to 384.16, rounded up to 385 whole respondents. Change the population field to a real number and the finite population correction divides that 385 down further, since a sample that size already covers a bigger share of a small group.
n0 = z squared times p times (1 minus p), divided by e squared, where e is your target margin as a decimal. The table below holds confidence and proportion at the common defaults (95%, p = 50%) and only moves the margin, straight from this calculator's own math:
Going from a 5% to a 1% margin costs roughly twenty-five times the respondents, not five. Related: the margin of error calculator runs this same formula forward, and the confidence interval calculator builds the interval once you have real data.
Leave it at the default 50%. You don't need to know the real answer in advance; 50% is the value that produces the largest, safest required sample regardless of how the actual results land, so planning around it protects you from under-sampling.
Nothing, until you enter a number above zero. At zero, the calculator assumes an effectively infinite population. Enter your real population and it applies the finite population correction, which shrinks the required sample once your sample would already cover a meaningful slice of a small group.
Margin of error sits in the denominator as e squared, so cutting the margin by a factor of five multiplies the required sample by roughly twenty-five. Small margins are expensive; the table above shows exactly how fast the sample grows.
Not directly. This formula sizes a single survey estimate against a margin of error. A true A/B test compares two proportions against each other and needs a different formula that accounts for both groups and the effect size you're trying to detect, which this tool does not implement.