How many responses does a survey actually need?
For estimating a proportion, approval, awareness, market share, the required sample size is set by three choices: the confidence level, the margin of error you can tolerate, and the proportion you expect (0.5 when unknown, the conservative choice, since p(1−p) peaks there). Population size is famously not on that list: a sample of 385 estimates a city's opinion and a continent's to the same ±5%, until the population is small enough that the finite-population correction starts trimming the requirement.
95% confidence, ±5% margin, p = 0.5: n = 385: the number behind nearly every national poll you have ever read. Surveying a staff of 10,000 with the same precision: the FPC trims it to 370. Tighten the margin to ±3% and the requirement jumps to 1,068, the square law collecting its tax, as always.
Sizing from the responses you hope to get rather than the precision you need, and forgetting nonresponse. If a third of invitees typically answer, invitations must be n ÷ 0.67, not n. The formula sizes completed responses.
Frequently asked questions
Why doesn't population size matter more?
Because precision depends on the absolute count sampled, not the fraction: tasting soup needs one spoon whatever the pot's size, provided the soup is stirred (the sample is random).
What p should I use if I have a rough expectation?
Use it: expecting 20% instead of planning for 50% cuts the required sample by more than a third. Just stay honest: if the true value lands nearer 0.5, your realised margin widens.